diff --git a/src/Numerics/LinearAlgebra/Double/DenseVector.cs b/src/Numerics/LinearAlgebra/Double/DenseVector.cs
index 0fe2ee50..a1d38288 100644
--- a/src/Numerics/LinearAlgebra/Double/DenseVector.cs
+++ b/src/Numerics/LinearAlgebra/Double/DenseVector.cs
@@ -341,6 +341,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Adds another vector to this vector.
         /// </summary>
         /// <param name="other">The vector to add to this one.</param>
+        /// <returns>A new vector containing the sum of both vectors.</returns>
         /// <exception cref="ArgumentNullException">If the other vector is <see langword="null" />.</exception> 
         /// <exception cref="ArgumentException">If this vector and <paramref name="other"/> are not the same size.</exception>
         public override Vector Add(Vector other)
@@ -359,11 +360,13 @@ namespace MathNet.Numerics.LinearAlgebra.Double
 
             if (denseVector == null)
             {
-                base.Add(other);
+                return base.Add(other);
             }
             else
             {
-                Control.LinearAlgebraProvider.AddVectorToScaledVector(Data, 1.0, denseVector.Data);
+                var copy = (DenseVector)this.Clone();
+                Control.LinearAlgebraProvider.AddVectorToScaledVector(copy.Data, 1.0, denseVector.Data);
+                return copy;
             }
         }
 
@@ -457,17 +460,20 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Subtracts a scalar from each element of the vector.
         /// </summary>
         /// <param name="scalar">The scalar to subtract.</param>
+        /// <returns>A new vector containing the subtraction of this vector and the scalar.</returns>
         public override Vector Subtract(double scalar)
         {
             if (scalar == 0.0)
             {
-                return;
+                return this.Clone();
             }
 
+            var copy = (DenseVector)this.Clone();
             CommonParallel.For(
                 0, 
                 Data.Length, 
-                index => Data[index] -= scalar);
+                index => copy.Data[index] -= scalar);
+            return copy;
         }
 
         /// <summary>
@@ -497,6 +503,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Subtracts another vector from this vector.
         /// </summary>
         /// <param name="other">The vector to subtract from this one.</param>
+        /// <returns>A new vector containing the subtraction of the the two vectors.</returns>
         /// <exception cref="ArgumentNullException">If the other vector is <see langword="null"/>.</exception>
         /// <exception cref="ArgumentException">If this vector and <paramref name="other"/> are not the same size.</exception>
         public override Vector Subtract(Vector other)
@@ -515,11 +522,13 @@ namespace MathNet.Numerics.LinearAlgebra.Double
 
             if (denseVector == null)
             {
-                base.Subtract(other);
+                return base.Subtract(other);
             }
             else
             {
-                Control.LinearAlgebraProvider.AddVectorToScaledVector(Data, -1.0, denseVector.Data);
+                var copy = (DenseVector)this.Clone();
+                Control.LinearAlgebraProvider.AddVectorToScaledVector(copy.Data, -1.0, denseVector.Data);
+                return copy;
             }
         }
 
@@ -628,14 +637,17 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Multiplies a scalar to each element of the vector.
         /// </summary>
         /// <param name="scalar">The scalar to multiply.</param>
+        /// <returns>A new vector that is the multiplication of the vector and the scalar.</returns>
         public override Vector Multiply(double scalar)
         {
             if (scalar == 1.0)
             {
-                return;
+                return this.Clone();
             }
 
-            Control.LinearAlgebraProvider.ScaleArray(scalar, Data);
+            var copy = (DenseVector)this.Clone();
+            Control.LinearAlgebraProvider.ScaleArray(scalar, copy.Data);
+            return copy;
         }
 
         /// <summary>
@@ -966,7 +978,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
 
             if (denseVector == null)
             {
-                base.PointwiseMultiply(other);
+                return base.PointwiseMultiply(other);
             }
             else
             {
@@ -1027,6 +1039,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Pointwise divide this vector with another vector.
         /// </summary>
         /// <param name="other">The vector to pointwise divide this one by.</param>
+        /// <returns>A new vector which is the pointwise division of the two vectors.</returns>
         /// <exception cref="ArgumentNullException">If the other vector is <see langword="null" />.</exception> 
         /// <exception cref="ArgumentException">If this vector and <paramref name="other"/> are not the same size.</exception>
         public override Vector PointwiseDivide(Vector other)
@@ -1045,14 +1058,16 @@ namespace MathNet.Numerics.LinearAlgebra.Double
 
             if (denseVector == null)
             {
-                base.PointwiseMultiply(other);
+                return base.PointwiseMultiply(other);
             }
             else
             {
+                var copy = (DenseVector)this.Clone();
                 CommonParallel.For(
                     0, 
-                    Count, 
-                    index => this[index] /= other[index]);
+                    Count,
+                    index => copy[index] /= other[index]);
+                return copy;
             }
         }
 
diff --git a/src/Numerics/LinearAlgebra/Double/SparseVector.cs b/src/Numerics/LinearAlgebra/Double/SparseVector.cs
index e50a416f..4ef3de1e 100644
--- a/src/Numerics/LinearAlgebra/Double/SparseVector.cs
+++ b/src/Numerics/LinearAlgebra/Double/SparseVector.cs
@@ -389,6 +389,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Adds another vector to this vector.
         /// </summary>
         /// <param name="other">The vector to add to this one.</param>
+        /// <returns>A new vector containing the sum of both vectors.</returns>
         /// <exception cref="ArgumentNullException">If the other vector is <see langword="null" />.</exception> 
         /// <exception cref="ArgumentException">If this vector and <paramref name="other"/> are not the same size.</exception>
         public override Vector Add(Vector other)
@@ -407,11 +408,13 @@ namespace MathNet.Numerics.LinearAlgebra.Double
 
             if (sparseVector == null)
             {
-                base.Add(other);
+                return base.Add(other);
             }
             else
             {
-                AddScaledSparceVector(1.0, sparseVector);
+                var copy = (SparseVector)this.Clone();
+                copy.AddScaledSparceVector(1.0, sparseVector);
+                return copy;
             }
         }
 
@@ -574,17 +577,20 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Subtracts a scalar from each element of the vector.
         /// </summary>
         /// <param name="scalar">The scalar to subtract.</param>
+        /// <returns>A new vector containing the subtraction of this vector and the scalar.</returns>
         public override Vector Subtract(double scalar)
         {
             if (scalar == 0.0)
             {
-                return;
+                return this.Clone();
             }
 
+            var copy = (SparseVector)this.Clone();
             for (var i = 0; i < Count; i++)
             {
-                this[i] -= scalar;
+                copy[i] -= scalar;
             }
+            return copy;
         }
 
         /// <summary>
@@ -614,6 +620,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Subtracts another vector from this vector.
         /// </summary>
         /// <param name="other">The vector to subtract from this one.</param>
+        /// <returns>A new vector containing the subtraction of the the two vectors.</returns>
         /// <exception cref="ArgumentNullException">If the other vector is <see langword="null"/>.</exception>
         /// <exception cref="ArgumentException">If this vector and <paramref name="other"/> are not the same size.</exception>
         public override Vector Subtract(Vector other)
@@ -632,11 +639,13 @@ namespace MathNet.Numerics.LinearAlgebra.Double
 
             if (sparseVector == null)
             {
-                base.Subtract(other);
+                return base.Subtract(other);
             }
             else
             {
-                AddScaledSparceVector(-1.0, sparseVector);
+                var copy = (SparseVector)this.Clone();
+                copy.AddScaledSparceVector(-1.0, sparseVector);
+                return copy;
             }
         }
 
@@ -753,20 +762,26 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Multiplies a scalar to each element of the vector.
         /// </summary>
         /// <param name="scalar">The scalar to multiply.</param>
+        /// <returns>A new vector that is the multiplication of the vector and the scalar.</returns>
         public override Vector Multiply(double scalar)
         {
             if (scalar == 1.0)
             {
-                return;
+                return this.Clone();
             }
-
-            if (scalar == 0)
+            else if (scalar == 0)
             {
-                Clear(); // Set array empty
-                return;
+                var copy = this.Clone();
+                copy.Clear(); // Set array empty
+                return copy;
             }
+            else
+            {
 
-            Control.LinearAlgebraProvider.ScaleArray(scalar, _nonZeroValues);
+                var copy = (SparseVector)this.Clone();
+                Control.LinearAlgebraProvider.ScaleArray(scalar, copy._nonZeroValues);
+                return copy;
+            }
         }
 
         /// <summary>
@@ -1128,6 +1143,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Pointwise divide this vector with another vector.
         /// </summary>
         /// <param name="other">The vector to pointwise divide this one by.</param>
+        /// <returns>A new vector which is the pointwise division of the two vectors.</returns>
         /// <exception cref="ArgumentNullException">If the other vector is <see langword="null" />.</exception> 
         /// <exception cref="ArgumentException">If this vector and <paramref name="other"/> are not the same size.</exception>
         public override Vector PointwiseDivide(Vector other)
@@ -1142,11 +1158,13 @@ namespace MathNet.Numerics.LinearAlgebra.Double
                 throw new ArgumentException(Resources.ArgumentVectorsSameLength, "other");
             }
 
-            // base implementation iterates though all elements, but we need only take non-zeros 
+            // base implementation iterates though all elements, but we need only take non-zeros
+            var copy = (SparseVector)this.Clone();
             for (var i = 0; i < NonZerosCount; i++)
             {
-                this[_nonZeroIndices[i]] /= other[_nonZeroIndices[i]];
+                copy[_nonZeroIndices[i]] /= other[_nonZeroIndices[i]];
             }
+            return copy;
         }
 
         /// <summary>
diff --git a/src/UnitTests/LinearAlgebraTests/Double/VectorTests.Arithmetic.cs b/src/UnitTests/LinearAlgebraTests/Double/VectorTests.Arithmetic.cs
index f3e2dca8..0935c711 100644
--- a/src/UnitTests/LinearAlgebraTests/Double/VectorTests.Arithmetic.cs
+++ b/src/UnitTests/LinearAlgebraTests/Double/VectorTests.Arithmetic.cs
@@ -60,8 +60,8 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double
         [MultipleAsserts]
         public void CanAddScalarToVector()
         {
-            var vector = this.CreateVector(this._data);
-            vector.Add(2.0);
+            var copy = this.CreateVector(this._data);
+            var vector = copy.Add(2.0);
 
             for (var i = 0; i < this._data.Length; i++)
             {
@@ -166,9 +166,9 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double
         [Test]
         public void CanAddTwoVectors()
         {
-            var vector = this.CreateVector(this._data);
+            var copy = this.CreateVector(this._data);
             var other = this.CreateVector(this._data);
-            vector.Add(other);
+            var vector = copy.Add(other);
 
             for (var i = 0; i < this._data.Length; i++)
             {
@@ -212,8 +212,8 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double
         [Test]
         public void CanAddVectorToItself()
         {
-            var vector = this.CreateVector(this._data);
-            vector.Add(vector);
+            var copy = this.CreateVector(this._data);
+            var vector = copy.Add(copy);
 
             for (var i = 0; i < this._data.Length; i++)
             {
@@ -285,8 +285,8 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double
         [MultipleAsserts]
         public void CanSubtractScalarFromVector()
         {
-            var vector = this.CreateVector(this._data);
-            vector.Subtract(2.0);
+            var copy = this.CreateVector(this._data);
+            var vector = copy.Subtract(2.0);
 
             for (var i = 0; i < this._data.Length; i++)
             {
@@ -391,9 +391,9 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double
         [Test]
         public void CanSubtractTwoVectors()
         {
-            var vector = this.CreateVector(this._data);
+            var copy = this.CreateVector(this._data);
             var other = this.CreateVector(this._data);
-            vector.Subtract(other);
+            var vector = copy.Subtract(other);
 
             for (var i = 0; i < this._data.Length; i++)
             {
@@ -437,8 +437,8 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double
         [Test]
         public void CanSubtractVectorFromItself()
         {
-            var vector = this.CreateVector(this._data);
-            vector.Subtract(vector);
+            var copy = this.CreateVector(this._data);
+            var vector = copy.Subtract(copy);
 
             for (var i = 0; i < this._data.Length; i++)
             {
@@ -480,8 +480,8 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double
         [MultipleAsserts]
         public void CanDivideVectorByScalar()
         {
-            var vector = this.CreateVector(this._data);
-            vector.Divide(2.0);
+            var copy = this.CreateVector(this._data);
+            var vector = copy.Divide(2.0);
 
             for (var i = 0; i < this._data.Length; i++)
             {
@@ -520,8 +520,8 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double
         [MultipleAsserts]
         public void CanMultiplyVectorByScalar()
         {
-            var vector = this.CreateVector(this._data);
-            vector.Multiply(2.0);
+            var copy = this.CreateVector(this._data);
+            var vector = copy.Multiply(2.0);
 
             for (var i = 0; i < this._data.Length; i++)
             {
@@ -725,6 +725,18 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double
 
         [Test]
         public void PointwiseMultiply()
+        {
+            var vector1 = this.CreateVector(this._data);
+            var vector2 = vector1.Clone();
+            var result = vector1.PointwiseMultiply(vector2);
+            for (var i = 0; i < vector1.Count; i++)
+            {
+                Assert.AreEqual(this._data[i] * this._data[i], result[i]);
+            }
+        }
+
+        [Test]
+        public void PointwiseMultiplyUsingResultVector()
         {
             var vector1 = this.CreateVector(this._data);
             var vector2 = vector1.Clone();
@@ -767,19 +779,19 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double
         }
 
         [Test]
-        public void PointWiseMultiplyWithResult()
+        public void PointWiseDivide()
         {
             var vector1 = this.CreateVector(this._data);
             var vector2 = vector1.Clone();
-            vector1.PointwiseMultiply(vector2);
+            var result = vector1.PointwiseDivide(vector2);
             for (var i = 0; i < vector1.Count; i++)
             {
-                Assert.AreEqual(this._data[i] * this._data[i], vector1[i]);
+                Assert.AreEqual(this._data[i] / this._data[i], result[i]);
             }
         }
        
         [Test]
-        public void PointWiseDivide()
+        public void PointWiseDivideUsingResultVector()
         {
             var vector1 = this.CreateVector(this._data);
             var vector2 = vector1.Clone();
@@ -821,18 +833,6 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double
             vector1.PointwiseDivide(vector2, result);
         }
 
-        [Test]
-        public void PointwiseDivideWithResult()
-        {
-            var vector1 = this.CreateVector(this._data);
-            var vector2 = vector1.Clone();
-            vector1.PointwiseDivide(vector2);
-            for (var i = 0; i < vector1.Count; i++)
-            {
-                Assert.AreEqual(this._data[i] / this._data[i], vector1[i]);
-            }
-        }
-
         [Test]
         public void CanCalculateOuterProduct()
         {