From bff2f68396d9739766ee64f9789783b9c702cf6c Mon Sep 17 00:00:00 2001
From: Christoph Ruegg <git@cdrnet.ch>
Date: Wed, 23 Oct 2013 20:32:42 +0200
Subject: [PATCH] LA: norml xml docs

---
 .../LinearAlgebra/Complex/DenseMatrix.cs      | 12 +++++-----
 .../LinearAlgebra/Complex/DiagonalMatrix.cs   | 16 ++++++-------
 src/Numerics/LinearAlgebra/Complex/Matrix.cs  | 12 +++++-----
 .../LinearAlgebra/Complex/SparseMatrix.cs     |  8 +++----
 .../LinearAlgebra/Complex32/DenseMatrix.cs    | 12 +++++-----
 .../LinearAlgebra/Complex32/DiagonalMatrix.cs | 20 ++++++++--------
 .../LinearAlgebra/Complex32/Matrix.cs         | 12 +++++-----
 .../LinearAlgebra/Complex32/SparseMatrix.cs   |  8 +++----
 .../LinearAlgebra/Double/DenseMatrix.cs       | 12 +++++-----
 .../LinearAlgebra/Double/DiagonalMatrix.cs    | 20 ++++++++--------
 src/Numerics/LinearAlgebra/Double/Matrix.cs   | 12 +++++-----
 .../LinearAlgebra/Double/SparseMatrix.cs      |  8 +++----
 .../LinearAlgebra/Matrix.Arithmetic.cs        | 24 +++++++++++--------
 .../LinearAlgebra/Single/DenseMatrix.cs       | 12 +++++-----
 .../LinearAlgebra/Single/DiagonalMatrix.cs    | 20 ++++++++--------
 src/Numerics/LinearAlgebra/Single/Matrix.cs   | 12 +++++-----
 .../LinearAlgebra/Single/SparseMatrix.cs      |  8 +++----
 17 files changed, 116 insertions(+), 112 deletions(-)

diff --git a/src/Numerics/LinearAlgebra/Complex/DenseMatrix.cs b/src/Numerics/LinearAlgebra/Complex/DenseMatrix.cs
index 66e7cbd6..7142e826 100644
--- a/src/Numerics/LinearAlgebra/Complex/DenseMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Complex/DenseMatrix.cs
@@ -426,22 +426,22 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
             return ret;
         }
 
-        /// <summary>Calculates the L1 norm.</summary>
-        /// <returns>The L1 norm of the matrix.</returns>
+        /// <summary>Calculates the induced L1 norm of this matrix.</summary>
+        /// <returns>The maximum absolute column sum of the matrix.</returns>
         public override double L1Norm()
         {
             return Control.LinearAlgebraProvider.MatrixNorm(Norm.OneNorm, _rowCount, _columnCount, _values);
         }
 
-        /// <summary>Calculates the infinity norm of this matrix.</summary>
-        /// <returns>The infinity norm of this matrix.</returns>
+        /// <summary>Calculates the induced infinity norm of this matrix.</summary>
+        /// <returns>The maximum absolute row sum of the matrix.</returns>
         public override double InfinityNorm()
         {
             return Control.LinearAlgebraProvider.MatrixNorm(Norm.InfinityNorm, _rowCount, _columnCount, _values);
         }
 
-        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
-        /// <returns>The Frobenius norm of this matrix.</returns>
+        /// <summary>Calculates the entry-wise Frobenius norm of this matrix.</summary>
+        /// <returns>The square root of the sum of the squared values.</returns>
         public override double FrobeniusNorm()
         {
             return Control.LinearAlgebraProvider.MatrixNorm(Norm.FrobeniusNorm, _rowCount, _columnCount, _values);
diff --git a/src/Numerics/LinearAlgebra/Complex/DiagonalMatrix.cs b/src/Numerics/LinearAlgebra/Complex/DiagonalMatrix.cs
index 29ee2201..d6a3e968 100644
--- a/src/Numerics/LinearAlgebra/Complex/DiagonalMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Complex/DiagonalMatrix.cs
@@ -652,22 +652,22 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
             return ret;
         }
 
-        /// <summary>Calculates the L1 norm.</summary>
-        /// <returns>The L1 norm of the matrix.</returns>
+        /// <summary>Calculates the induced L1 norm of this matrix.</summary>
+        /// <returns>The maximum absolute column sum of the matrix.</returns>
         public override double L1Norm()
         {
-            return _data.Aggregate(double.NegativeInfinity, (current, t) => Math.Max(current, t.Magnitude));
+            return _data.Aggregate(0d, (current, t) => Math.Max(current, t.Magnitude));
         }
 
-        /// <summary>Calculates the L2 norm.</summary>
-        /// <returns>The L2 norm of the matrix.</returns>
+        /// <summary>Calculates the induced L2 norm of the matrix.</summary>
+        /// <returns>The largest singular value of the matrix.</returns>
         public override double L2Norm()
         {
-            return _data.Aggregate(double.NegativeInfinity, (current, t) => Math.Max(current, t.Magnitude));
+            return _data.Aggregate(0d, (current, t) => Math.Max(current, t.Magnitude));
         }
 
-        /// <summary>Calculates the infinity norm of this matrix.</summary>
-        /// <returns>The infinity norm of this matrix.</returns>
+        /// <summary>Calculates the induced infinity norm of this matrix.</summary>
+        /// <returns>The maximum absolute row sum of the matrix.</returns>
         public override double InfinityNorm()
         {
             return L1Norm();
diff --git a/src/Numerics/LinearAlgebra/Complex/Matrix.cs b/src/Numerics/LinearAlgebra/Complex/Matrix.cs
index afebdc5f..75c1412d 100644
--- a/src/Numerics/LinearAlgebra/Complex/Matrix.cs
+++ b/src/Numerics/LinearAlgebra/Complex/Matrix.cs
@@ -57,8 +57,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
         {
         }
 
-        /// <summary>Calculates the L1 norm.</summary>
-        /// <returns>The L1 norm of the matrix.</returns>
+        /// <summary>Calculates the induced L1 norm of this matrix.</summary>
+        /// <returns>The maximum absolute column sum of the matrix.</returns>
         public override double L1Norm()
         {
             var norm = 0d;
@@ -74,8 +74,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
             return norm;
         }
 
-        /// <summary>Calculates the infinity norm of this matrix.</summary>
-        /// <returns>The infinity norm of this matrix.</returns>   
+        /// <summary>Calculates the induced infinity norm of this matrix.</summary>
+        /// <returns>The maximum absolute row sum of the matrix.</returns>
         public override double InfinityNorm()
         {
             var norm = 0d;
@@ -91,8 +91,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
             return norm;
         }
 
-        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
-        /// <returns>The Frobenius norm of this matrix.</returns>
+        /// <summary>Calculates the entry-wise Frobenius norm of this matrix.</summary>
+        /// <returns>The square root of the sum of the squared values.</returns>
         public override double FrobeniusNorm()
         {
             var transpose = ConjugateTranspose();
diff --git a/src/Numerics/LinearAlgebra/Complex/SparseMatrix.cs b/src/Numerics/LinearAlgebra/Complex/SparseMatrix.cs
index b2c2d1dc..02daadea 100644
--- a/src/Numerics/LinearAlgebra/Complex/SparseMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Complex/SparseMatrix.cs
@@ -674,8 +674,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
             return new SparseMatrix(ret);
         }
 
-        /// <summary>Calculates the infinity norm of this matrix.</summary>
-        /// <returns>The infinity norm of this matrix.</returns>
+        /// <summary>Calculates the induced infinity norm of this matrix.</summary>
+        /// <returns>The maximum absolute row sum of the matrix.</returns>
         public override double InfinityNorm()
         {
             var rowPointers = _storage.RowPointers;
@@ -701,8 +701,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
             return norm;
         }
 
-        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
-        /// <returns>The Frobenius norm of this matrix.</returns>
+        /// <summary>Calculates the entry-wise Frobenius norm of this matrix.</summary>
+        /// <returns>The square root of the sum of the squared values.</returns>
         public override double FrobeniusNorm()
         {
             var aat = (SparseCompressedRowMatrixStorage<Complex>) (this*ConjugateTranspose()).Storage;
diff --git a/src/Numerics/LinearAlgebra/Complex32/DenseMatrix.cs b/src/Numerics/LinearAlgebra/Complex32/DenseMatrix.cs
index 10f5cbe7..df9a2192 100644
--- a/src/Numerics/LinearAlgebra/Complex32/DenseMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Complex32/DenseMatrix.cs
@@ -421,22 +421,22 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
             return ret;
         }
 
-        /// <summary>Calculates the L1 norm.</summary>
-        /// <returns>The L1 norm of the matrix.</returns>
+        /// <summary>Calculates the induced L1 norm of this matrix.</summary>
+        /// <returns>The maximum absolute column sum of the matrix.</returns>
         public override double L1Norm()
         {
             return Control.LinearAlgebraProvider.MatrixNorm(Norm.OneNorm, _rowCount, _columnCount, _values);
         }
 
-        /// <summary>Calculates the infinity norm of this matrix.</summary>
-        /// <returns>The infinity norm of this matrix.</returns>
+        /// <summary>Calculates the induced infinity norm of this matrix.</summary>
+        /// <returns>The maximum absolute row sum of the matrix.</returns>
         public override double InfinityNorm()
         {
             return Control.LinearAlgebraProvider.MatrixNorm(Norm.InfinityNorm, _rowCount, _columnCount, _values);
         }
 
-        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
-        /// <returns>The Frobenius norm of this matrix.</returns>
+        /// <summary>Calculates the entry-wise Frobenius norm of this matrix.</summary>
+        /// <returns>The square root of the sum of the squared values.</returns>
         public override double FrobeniusNorm()
         {
             return Control.LinearAlgebraProvider.MatrixNorm(Norm.FrobeniusNorm, _rowCount, _columnCount, _values);
diff --git a/src/Numerics/LinearAlgebra/Complex32/DiagonalMatrix.cs b/src/Numerics/LinearAlgebra/Complex32/DiagonalMatrix.cs
index d1bde21a..f1f04d3b 100644
--- a/src/Numerics/LinearAlgebra/Complex32/DiagonalMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Complex32/DiagonalMatrix.cs
@@ -647,29 +647,29 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
             return ret;
         }
 
-        /// <summary>Calculates the L1 norm.</summary>
-        /// <returns>The L1 norm of the matrix.</returns>
+        /// <summary>Calculates the induced L1 norm of this matrix.</summary>
+        /// <returns>The maximum absolute column sum of the matrix.</returns>
         public override double L1Norm()
         {
-            return _data.Aggregate(float.NegativeInfinity, (current, t) => Math.Max(current, t.Magnitude));
+            return _data.Aggregate(0f, (current, t) => Math.Max(current, t.Magnitude));
         }
 
-        /// <summary>Calculates the L2 norm.</summary>
-        /// <returns>The L2 norm of the matrix.</returns>
+        /// <summary>Calculates the induced L2 norm of the matrix.</summary>
+        /// <returns>The largest singular value of the matrix.</returns>
         public override double L2Norm()
         {
-            return _data.Aggregate(float.NegativeInfinity, (current, t) => Math.Max(current, t.Magnitude));
+            return _data.Aggregate(0f, (current, t) => Math.Max(current, t.Magnitude));
         }
 
-        /// <summary>Calculates the infinity norm of this matrix.</summary>
-        /// <returns>The infinity norm of this matrix.</returns>
+        /// <summary>Calculates the induced infinity norm of this matrix.</summary>
+        /// <returns>The maximum absolute row sum of the matrix.</returns>
         public override double InfinityNorm()
         {
             return L1Norm();
         }
 
-        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
-        /// <returns>The Frobenius norm of this matrix.</returns>
+        /// <summary>Calculates the entry-wise Frobenius norm of this matrix.</summary>
+        /// <returns>The square root of the sum of the squared values.</returns>
         public override double FrobeniusNorm()
         {
             return Math.Sqrt(_data.Sum(t => t.Magnitude * t.Magnitude));
diff --git a/src/Numerics/LinearAlgebra/Complex32/Matrix.cs b/src/Numerics/LinearAlgebra/Complex32/Matrix.cs
index 2ab02f16..ad6a3346 100644
--- a/src/Numerics/LinearAlgebra/Complex32/Matrix.cs
+++ b/src/Numerics/LinearAlgebra/Complex32/Matrix.cs
@@ -52,8 +52,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
         {
         }
 
-        /// <summary>Calculates the L1 norm.</summary>
-        /// <returns>The L1 norm of the matrix.</returns>
+        /// <summary>Calculates the induced L1 norm of this matrix.</summary>
+        /// <returns>The maximum absolute column sum of the matrix.</returns>
         public override double L1Norm()
         {
             var norm = 0d;
@@ -69,8 +69,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
             return norm;
         }
 
-        /// <summary>Calculates the infinity norm of this matrix.</summary>
-        /// <returns>The infinity norm of this matrix.</returns>
+        /// <summary>Calculates the induced infinity norm of this matrix.</summary>
+        /// <returns>The maximum absolute row sum of the matrix.</returns>
         public override double InfinityNorm()
         {
             var norm = 0d;
@@ -86,8 +86,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
             return norm;
         }
 
-        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
-        /// <returns>The Frobenius norm of this matrix.</returns>
+        /// <summary>Calculates the entry-wise Frobenius norm of this matrix.</summary>
+        /// <returns>The square root of the sum of the squared values.</returns>
         public override double FrobeniusNorm()
         {
             var transpose = ConjugateTranspose();
diff --git a/src/Numerics/LinearAlgebra/Complex32/SparseMatrix.cs b/src/Numerics/LinearAlgebra/Complex32/SparseMatrix.cs
index 84a2e9fb..2b6a13bf 100644
--- a/src/Numerics/LinearAlgebra/Complex32/SparseMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Complex32/SparseMatrix.cs
@@ -669,8 +669,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
             return new SparseMatrix(ret);
         }
 
-        /// <summary>Calculates the infinity norm of this matrix.</summary>
-        /// <returns>The infinity norm of this matrix.</returns>
+        /// <summary>Calculates the induced infinity norm of this matrix.</summary>
+        /// <returns>The maximum absolute row sum of the matrix.</returns>
         public override double InfinityNorm()
         {
             var rowPointers = _storage.RowPointers;
@@ -696,8 +696,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
             return norm;
         }
 
-        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
-        /// <returns>The Frobenius norm of this matrix.</returns>
+        /// <summary>Calculates the entry-wise Frobenius norm of this matrix.</summary>
+        /// <returns>The square root of the sum of the squared values.</returns>
         public override double FrobeniusNorm()
         {
             var aat = (SparseCompressedRowMatrixStorage<Complex32>) (this*ConjugateTranspose()).Storage;
diff --git a/src/Numerics/LinearAlgebra/Double/DenseMatrix.cs b/src/Numerics/LinearAlgebra/Double/DenseMatrix.cs
index c7169274..30198a63 100644
--- a/src/Numerics/LinearAlgebra/Double/DenseMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Double/DenseMatrix.cs
@@ -418,22 +418,22 @@ namespace MathNet.Numerics.LinearAlgebra.Double
             return ret;
         }
 
-        /// <summary>Calculates the L1 norm.</summary>
-        /// <returns>The L1 norm of the matrix.</returns>
+        /// <summary>Calculates the induced L1 norm of this matrix.</summary>
+        /// <returns>The maximum absolute column sum of the matrix.</returns>
         public override double L1Norm()
         {
             return Control.LinearAlgebraProvider.MatrixNorm(Norm.OneNorm, _rowCount, _columnCount, _values);
         }
 
-        /// <summary>Calculates the infinity norm of this matrix.</summary>
-        /// <returns>The infinity norm of this matrix.</returns>
+        /// <summary>Calculates the induced infinity norm of this matrix.</summary>
+        /// <returns>The maximum absolute row sum of the matrix.</returns>
         public override double InfinityNorm()
         {
             return Control.LinearAlgebraProvider.MatrixNorm(Norm.InfinityNorm, _rowCount, _columnCount, _values);
         }
 
-        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
-        /// <returns>The Frobenius norm of this matrix.</returns>
+        /// <summary>Calculates the entry-wise Frobenius norm of this matrix.</summary>
+        /// <returns>The square root of the sum of the squared values.</returns>
         public override double FrobeniusNorm()
         {
             return Control.LinearAlgebraProvider.MatrixNorm(Norm.FrobeniusNorm, _rowCount, _columnCount, _values);
diff --git a/src/Numerics/LinearAlgebra/Double/DiagonalMatrix.cs b/src/Numerics/LinearAlgebra/Double/DiagonalMatrix.cs
index cbad50e0..e489a675 100644
--- a/src/Numerics/LinearAlgebra/Double/DiagonalMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Double/DiagonalMatrix.cs
@@ -641,29 +641,29 @@ namespace MathNet.Numerics.LinearAlgebra.Double
             return ret;
         }
 
-        /// <summary>Calculates the L1 norm.</summary>
-        /// <returns>The L1 norm of the matrix.</returns>
+        /// <summary>Calculates the induced L1 norm of this matrix.</summary>
+        /// <returns>The maximum absolute column sum of the matrix.</returns>
         public override double L1Norm()
         {
-            return _data.Aggregate(double.NegativeInfinity, (current, t) => Math.Max(current, Math.Abs(t)));
+            return _data.Aggregate(0d, (current, t) => Math.Max(current, Math.Abs(t)));
         }
 
-        /// <summary>Calculates the L2 norm.</summary>
-        /// <returns>The L2 norm of the matrix.</returns>
+        /// <summary>Calculates the induced L2 norm of the matrix.</summary>
+        /// <returns>The largest singular value of the matrix.</returns>
         public override double L2Norm()
         {
-            return _data.Aggregate(double.NegativeInfinity, (current, t) => Math.Max(current, Math.Abs(t)));
+            return _data.Aggregate(0d, (current, t) => Math.Max(current, Math.Abs(t)));
         }
 
-        /// <summary>Calculates the infinity norm of this matrix.</summary>
-        /// <returns>The infinity norm of this matrix.</returns>
+        /// <summary>Calculates the induced infinity norm of this matrix.</summary>
+        /// <returns>The maximum absolute row sum of the matrix.</returns>
         public override double InfinityNorm()
         {
             return L1Norm();
         }
 
-        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
-        /// <returns>The Frobenius norm of this matrix.</returns>
+        /// <summary>Calculates the entry-wise Frobenius norm of this matrix.</summary>
+        /// <returns>The square root of the sum of the squared values.</returns>
         public override double FrobeniusNorm()
         {
             return Math.Sqrt(_data.Sum(t => t * t));
diff --git a/src/Numerics/LinearAlgebra/Double/Matrix.cs b/src/Numerics/LinearAlgebra/Double/Matrix.cs
index bc4fa558..ec4eaa25 100644
--- a/src/Numerics/LinearAlgebra/Double/Matrix.cs
+++ b/src/Numerics/LinearAlgebra/Double/Matrix.cs
@@ -50,8 +50,8 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         {
         }
 
-        /// <summary>Calculates the L1 norm.</summary>
-        /// <returns>The L1 norm of the matrix.</returns>
+        /// <summary>Calculates the induced L1 norm of this matrix.</summary>
+        /// <returns>The maximum absolute column sum of the matrix.</returns>
         public override double L1Norm()
         {
             var norm = 0d;
@@ -67,8 +67,8 @@ namespace MathNet.Numerics.LinearAlgebra.Double
             return norm;
         }
 
-        /// <summary>Calculates the infinity norm of this matrix.</summary>
-        /// <returns>The infinity norm of this matrix.</returns>   
+        /// <summary>Calculates the induced infinity norm of this matrix.</summary>
+        /// <returns>The maximum absolute row sum of the matrix.</returns>
         public override double InfinityNorm()
         {
             var norm = 0d;
@@ -84,8 +84,8 @@ namespace MathNet.Numerics.LinearAlgebra.Double
             return norm;
         }
 
-        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
-        /// <returns>The Frobenius norm of this matrix.</returns>
+        /// <summary>Calculates the entry-wise Frobenius norm of this matrix.</summary>
+        /// <returns>The square root of the sum of the squared values.</returns>
         public override double FrobeniusNorm()
         {
             var transpose = Transpose();
diff --git a/src/Numerics/LinearAlgebra/Double/SparseMatrix.cs b/src/Numerics/LinearAlgebra/Double/SparseMatrix.cs
index e67972fa..80a1cf4b 100644
--- a/src/Numerics/LinearAlgebra/Double/SparseMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Double/SparseMatrix.cs
@@ -668,8 +668,8 @@ namespace MathNet.Numerics.LinearAlgebra.Double
             return new SparseMatrix(ret);
         }
 
-        /// <summary>Calculates the infinity norm of this matrix.</summary>
-        /// <returns>The infinity norm of this matrix.</returns>
+        /// <summary>Calculates the induced infinity norm of this matrix.</summary>
+        /// <returns>The maximum absolute row sum of the matrix.</returns>
         public override double InfinityNorm()
         {
             var rowPointers = _storage.RowPointers;
@@ -696,8 +696,8 @@ namespace MathNet.Numerics.LinearAlgebra.Double
             return norm;
         }
 
-        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
-        /// <returns>The Frobenius norm of this matrix.</returns>
+        /// <summary>Calculates the entry-wise Frobenius norm of this matrix.</summary>
+        /// <returns>The square root of the sum of the squared values.</returns>
         public override double FrobeniusNorm()
         {
             var aat = (SparseCompressedRowMatrixStorage<double>) (this*Transpose()).Storage;
diff --git a/src/Numerics/LinearAlgebra/Matrix.Arithmetic.cs b/src/Numerics/LinearAlgebra/Matrix.Arithmetic.cs
index 54ef95d5..25163d6a 100644
--- a/src/Numerics/LinearAlgebra/Matrix.Arithmetic.cs
+++ b/src/Numerics/LinearAlgebra/Matrix.Arithmetic.cs
@@ -1148,27 +1148,31 @@ namespace MathNet.Numerics.LinearAlgebra
             return ret;
         }
 
-        /// <summary>Calculates the L1 norm.</summary>
-        /// <returns>The L1 norm of the matrix.</returns>
+        /// <summary>Calculates the induced L1 norm of this matrix.</summary>
+        /// <returns>The maximum absolute column sum of the matrix.</returns>
         public abstract double L1Norm();
 
-        /// <summary>Calculates the L2 norm.</summary>
-        /// <returns>The L2 norm of the matrix.</returns>
-        /// <remarks>For sparse matrices, the L2 norm is computed using a dense implementation of singular value decomposition.
-        /// In a later release, it will be replaced with a sparse implementation.</remarks>
+        /// <summary>Calculates the induced L2 norm of the matrix.</summary>
+        /// <returns>The largest singular value of the matrix.</returns>
+        /// <remarks>
+        /// For sparse matrices, the L2 norm is computed using a dense implementation of singular value decomposition.
+        /// In a later release, it will be replaced with a sparse implementation.
+        /// </remarks>
         public virtual double L2Norm()
         {
             return Svd(false).L2Norm;
         }
 
-        /// <summary>Calculates the infinity norm of this matrix.</summary>
-        /// <returns>The infinity norm of this matrix.</returns>
+        /// <summary>Calculates the induced infinity norm of this matrix.</summary>
+        /// <returns>The maximum absolute row sum of the matrix.</returns>
         public abstract double InfinityNorm();
 
-        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
-        /// <returns>The Frobenius norm of this matrix.</returns>
+        /// <summary>Calculates the entry-wise Frobenius norm of this matrix.</summary>
+        /// <returns>The square root of the sum of the squared values.</returns>
         public abstract double FrobeniusNorm();
 
+
+
         #region Exceptions - possibly move elsewhere?
 
         internal static Exception DimensionsDontMatch<TException>(Matrix<T> left, Matrix<T> right, Matrix<T> result, string paramName = null)
diff --git a/src/Numerics/LinearAlgebra/Single/DenseMatrix.cs b/src/Numerics/LinearAlgebra/Single/DenseMatrix.cs
index ce6407c1..8c3417ee 100644
--- a/src/Numerics/LinearAlgebra/Single/DenseMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Single/DenseMatrix.cs
@@ -418,22 +418,22 @@ namespace MathNet.Numerics.LinearAlgebra.Single
             return ret;
         }
 
-        /// <summary>Calculates the L1 norm.</summary>
-        /// <returns>The L1 norm of the matrix.</returns>
+        /// <summary>Calculates the induced L1 norm of this matrix.</summary>
+        /// <returns>The maximum absolute column sum of the matrix.</returns>
         public override double L1Norm()
         {
             return Control.LinearAlgebraProvider.MatrixNorm(Norm.OneNorm, _rowCount, _columnCount, _values);
         }
 
-        /// <summary>Calculates the infinity norm of this matrix.</summary>
-        /// <returns>The infinity norm of this matrix.</returns>
+        /// <summary>Calculates the induced infinity norm of this matrix.</summary>
+        /// <returns>The maximum absolute row sum of the matrix.</returns>
         public override double InfinityNorm()
         {
             return Control.LinearAlgebraProvider.MatrixNorm(Norm.InfinityNorm, _rowCount, _columnCount, _values);
         }
 
-        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
-        /// <returns>The Frobenius norm of this matrix.</returns>
+        /// <summary>Calculates the entry-wise Frobenius norm of this matrix.</summary>
+        /// <returns>The square root of the sum of the squared values.</returns>
         public override double FrobeniusNorm()
         {
             return Control.LinearAlgebraProvider.MatrixNorm(Norm.FrobeniusNorm, _rowCount, _columnCount, _values);
diff --git a/src/Numerics/LinearAlgebra/Single/DiagonalMatrix.cs b/src/Numerics/LinearAlgebra/Single/DiagonalMatrix.cs
index 41b87d71..e388e2b2 100644
--- a/src/Numerics/LinearAlgebra/Single/DiagonalMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Single/DiagonalMatrix.cs
@@ -641,29 +641,29 @@ namespace MathNet.Numerics.LinearAlgebra.Single
             return ret;
         }
 
-        /// <summary>Calculates the L1 norm.</summary>
-        /// <returns>The L1 norm of the matrix.</returns>
+        /// <summary>Calculates the induced L1 norm of this matrix.</summary>
+        /// <returns>The maximum absolute column sum of the matrix.</returns>
         public override double L1Norm()
         {
-            return _data.Aggregate(float.NegativeInfinity, (current, t) => Math.Max(current, Math.Abs(t)));
+            return _data.Aggregate(0f, (current, t) => Math.Max(current, Math.Abs(t)));
         }
 
-        /// <summary>Calculates the L2 norm.</summary>
-        /// <returns>The L2 norm of the matrix.</returns>
+        /// <summary>Calculates the induced L2 norm of the matrix.</summary>
+        /// <returns>The largest singular value of the matrix.</returns>
         public override double L2Norm()
         {
-            return _data.Aggregate(float.NegativeInfinity, (current, t) => Math.Max(current, Math.Abs(t)));
+            return _data.Aggregate(0f, (current, t) => Math.Max(current, Math.Abs(t)));
         }
 
-        /// <summary>Calculates the infinity norm of this matrix.</summary>
-        /// <returns>The infinity norm of this matrix.</returns>
+        /// <summary>Calculates the induced infinity norm of this matrix.</summary>
+        /// <returns>The maximum absolute row sum of the matrix.</returns>
         public override double InfinityNorm()
         {
             return L1Norm();
         }
 
-        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
-        /// <returns>The Frobenius norm of this matrix.</returns>
+        /// <summary>Calculates the entry-wise Frobenius norm of this matrix.</summary>
+        /// <returns>The square root of the sum of the squared values.</returns>
         public override double FrobeniusNorm()
         {
             return Math.Sqrt(_data.Sum(t => t * t));
diff --git a/src/Numerics/LinearAlgebra/Single/Matrix.cs b/src/Numerics/LinearAlgebra/Single/Matrix.cs
index 902b86ff..761734f0 100644
--- a/src/Numerics/LinearAlgebra/Single/Matrix.cs
+++ b/src/Numerics/LinearAlgebra/Single/Matrix.cs
@@ -50,8 +50,8 @@ namespace MathNet.Numerics.LinearAlgebra.Single
         {
         }
 
-        /// <summary>Calculates the L1 norm.</summary>
-        /// <returns>The L1 norm of the matrix.</returns>
+        /// <summary>Calculates the induced L1 norm of this matrix.</summary>
+        /// <returns>The maximum absolute column sum of the matrix.</returns>
         public override double L1Norm()
         {
             var norm = 0d;
@@ -67,8 +67,8 @@ namespace MathNet.Numerics.LinearAlgebra.Single
             return norm;
         }
 
-        /// <summary>Calculates the infinity norm of this matrix.</summary>
-        /// <returns>The infinity norm of this matrix.</returns>   
+        /// <summary>Calculates the induced infinity norm of this matrix.</summary>
+        /// <returns>The maximum absolute row sum of the matrix.</returns>
         public override double InfinityNorm()
         {
             var norm = 0d;
@@ -84,8 +84,8 @@ namespace MathNet.Numerics.LinearAlgebra.Single
             return norm;
         }
 
-        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
-        /// <returns>The Frobenius norm of this matrix.</returns>
+        /// <summary>Calculates the entry-wise Frobenius norm of this matrix.</summary>
+        /// <returns>The square root of the sum of the squared values.</returns>
         public override double FrobeniusNorm()
         {
             var transpose = Transpose();
diff --git a/src/Numerics/LinearAlgebra/Single/SparseMatrix.cs b/src/Numerics/LinearAlgebra/Single/SparseMatrix.cs
index 6454d1a5..ca0bc1ed 100644
--- a/src/Numerics/LinearAlgebra/Single/SparseMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Single/SparseMatrix.cs
@@ -670,8 +670,8 @@ namespace MathNet.Numerics.LinearAlgebra.Single
             return new SparseMatrix(ret);
         }
 
-        /// <summary>Calculates the infinity norm of this matrix.</summary>
-        /// <returns>The infinity norm of this matrix.</returns>
+        /// <summary>Calculates the induced infinity norm of this matrix.</summary>
+        /// <returns>The maximum absolute row sum of the matrix.</returns>
         public override double InfinityNorm()
         {
             var rowPointers = _storage.RowPointers;
@@ -700,8 +700,8 @@ namespace MathNet.Numerics.LinearAlgebra.Single
             return norm;
         }
 
-        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
-        /// <returns>The Frobenius norm of this matrix.</returns>
+        /// <summary>Calculates the entry-wise Frobenius norm of this matrix.</summary>
+        /// <returns>The square root of the sum of the squared values.</returns>
         public override double FrobeniusNorm()
         {
             var aat = (SparseCompressedRowMatrixStorage<float>) (this*Transpose()).Storage;