diff --git a/src/Numerics/LinearAlgebra/Double/DenseVector.cs b/src/Numerics/LinearAlgebra/Double/DenseVector.cs
index 4a8d7cb9..0fe2ee50 100644
--- a/src/Numerics/LinearAlgebra/Double/DenseVector.cs
+++ b/src/Numerics/LinearAlgebra/Double/DenseVector.cs
@@ -298,17 +298,20 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Adds a scalar to each element of the vector.
         /// </summary>
         /// <param name="scalar">The scalar to add.</param>
-        public override void Add(double scalar)
+        /// <returns>A copy of the vector with the scalar added.</returns>
+        public override Vector Add(double scalar)
         {
             if (scalar == 0.0)
             {
-                return;
+                return this.Clone();
             }
 
+            var copy = (DenseVector) this.Clone();
             CommonParallel.For(
                 0, 
-                Data.Length, 
-                index => Data[index] += scalar);
+                Data.Length,
+                index => copy.Data[index] += scalar);
+            return copy;
         }
 
         /// <summary>
@@ -340,7 +343,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// <param name="other">The vector to add to this one.</param>
         /// <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 void Add(Vector other)
+        public override Vector Add(Vector other)
         {
             if (other == null)
             {
@@ -454,7 +457,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Subtracts a scalar from each element of the vector.
         /// </summary>
         /// <param name="scalar">The scalar to subtract.</param>
-        public override void Subtract(double scalar)
+        public override Vector Subtract(double scalar)
         {
             if (scalar == 0.0)
             {
@@ -496,7 +499,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// <param name="other">The vector to subtract from this one.</param>
         /// <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 void Subtract(Vector other)
+        public override Vector Subtract(Vector other)
         {
             if (other == null)
             {
@@ -625,7 +628,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Multiplies a scalar to each element of the vector.
         /// </summary>
         /// <param name="scalar">The scalar to multiply.</param>
-        public override void Multiply(double scalar)
+        public override Vector Multiply(double scalar)
         {
             if (scalar == 1.0)
             {
@@ -944,9 +947,10 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Pointwise multiplies this vector with another vector.
         /// </summary>
         /// <param name="other">The vector to pointwise multiply with this one.</param>
+        /// <returns>A new vector which is the pointwise multiplication 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 void PointwiseMultiply(Vector other)
+        public override Vector PointwiseMultiply(Vector other)
         {
             if (other == null)
             {
@@ -966,10 +970,12 @@ namespace MathNet.Numerics.LinearAlgebra.Double
             }
             else
             {
+                var copy = (DenseVector)this.Clone();
                 CommonParallel.For(
                     0, 
-                    Count, 
-                    index => this[index] *= other[index]);
+                    Count,
+                    index => copy[index] *= other[index]);
+                return copy;
             }
         }
 
@@ -1023,7 +1029,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// <param name="other">The vector to pointwise divide this one by.</param>
         /// <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 void PointwiseDivide(Vector other)
+        public override Vector PointwiseDivide(Vector other)
         {
             if (other == null)
             {
diff --git a/src/Numerics/LinearAlgebra/Double/SparseVector.cs b/src/Numerics/LinearAlgebra/Double/SparseVector.cs
index 8a386359..e50a416f 100644
--- a/src/Numerics/LinearAlgebra/Double/SparseVector.cs
+++ b/src/Numerics/LinearAlgebra/Double/SparseVector.cs
@@ -346,17 +346,20 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Adds a scalar to each element of the vector.
         /// </summary>
         /// <param name="scalar">The scalar to add.</param>
-        public override void Add(double scalar)
+        /// <returns>A copy of the vector with the scalar added.</returns>
+        public override Vector Add(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>
@@ -388,7 +391,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// <param name="other">The vector to add to this one.</param>
         /// <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 void Add(Vector other)
+        public override Vector Add(Vector other)
         {
             if (other == null)
             {
@@ -571,7 +574,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Subtracts a scalar from each element of the vector.
         /// </summary>
         /// <param name="scalar">The scalar to subtract.</param>
-        public override void Subtract(double scalar)
+        public override Vector Subtract(double scalar)
         {
             if (scalar == 0.0)
             {
@@ -613,7 +616,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// <param name="other">The vector to subtract from this one.</param>
         /// <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 void Subtract(Vector other)
+        public override Vector Subtract(Vector other)
         {
             if (other == null)
             {
@@ -750,7 +753,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Multiplies a scalar to each element of the vector.
         /// </summary>
         /// <param name="scalar">The scalar to multiply.</param>
-        public override void Multiply(double scalar)
+        public override Vector Multiply(double scalar)
         {
             if (scalar == 1.0)
             {
@@ -1053,9 +1056,10 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Pointwise multiplies this vector with another vector.
         /// </summary>
         /// <param name="other">The vector to pointwise multiply with this one.</param>
+        /// <returns>A new vector which is the pointwise multiplication 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 void PointwiseMultiply(Vector other)
+        public override Vector PointwiseMultiply(Vector other)
         {
             if (other == null)
             {
@@ -1068,10 +1072,12 @@ namespace MathNet.Numerics.LinearAlgebra.Double
             }
 
             // We cannot iterate using NonZeroCount because the value may be changed (if multiply by 0)
+            var copy = (SparseVector)this.Clone();
             for (var i = 0; i < Count; i++)
             {
-                this[i] *= other[i];
+                copy[i] *= other[i];
             }
+            return copy;
         }
 
         /// <summary>
@@ -1124,7 +1130,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// <param name="other">The vector to pointwise divide this one by.</param>
         /// <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 void PointwiseDivide(Vector other)
+        public override Vector PointwiseDivide(Vector other)
         {
             if (other == null)
             {
diff --git a/src/Numerics/LinearAlgebra/Double/Vector.cs b/src/Numerics/LinearAlgebra/Double/Vector.cs
index 60831009..e5341d1e 100644
--- a/src/Numerics/LinearAlgebra/Double/Vector.cs
+++ b/src/Numerics/LinearAlgebra/Double/Vector.cs
@@ -120,17 +120,20 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// <param name="scalar">
         /// The scalar to add.
         /// </param>
-        public virtual void Add(double scalar)
+        /// <returns>A copy of the vector with the scalar added.</returns>
+        public virtual Vector Add(double scalar)
         {
             if (scalar == 0.0)
             {
-                return;
+                return this.Clone();
             }
 
+            var copy = this.Clone();
             CommonParallel.For(
                 0, 
-                Count, 
-                index => this[index] += scalar);
+                Count,
+                index => copy[index] += scalar);
+            return copy;
         }
 
         /// <summary>
@@ -169,7 +172,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         }
 
         /// <summary>
-        /// Returns this vector.
+        /// Returns a copy of this vector.
         /// </summary>
         /// <returns>
         /// This vector.
@@ -179,7 +182,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// </remarks>
         public virtual Vector Plus()
         {
-            return this;
+            return this * 1.0;
         }
 
         /// <summary>
@@ -188,13 +191,14 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// <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 virtual void Add(Vector other)
+        public virtual Vector Add(Vector other)
         {
             if (other == null)
             {
@@ -206,10 +210,12 @@ namespace MathNet.Numerics.LinearAlgebra.Double
                 throw new ArgumentException(Resources.ArgumentVectorsSameLength, "other");
             }
 
+            var copy = this.Clone();
             CommonParallel.For(
                 0, 
-                Count, 
-                index => this[index] += other[index]);
+                Count,
+                index => copy[index] += other[index]);
+            return copy;
         }
 
         /// <summary>
@@ -264,17 +270,20 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// <param name="scalar">
         /// The scalar to subtract.
         /// </param>
-        public virtual void Subtract(double scalar)
+        /// <returns>A new vector containing the subtraction of this vector and the scalar.</returns>
+        public virtual Vector Subtract(double scalar)
         {
             if (scalar == 0.0)
             {
-                return;
+                return this.Clone();
             }
 
+            var copy = this.Clone();
             CommonParallel.For(
                 0, 
                 Count, 
-                index => this[index] -= scalar);
+                index => copy[index] -= scalar);
+            return copy;
         }
 
         /// <summary>
@@ -332,13 +341,14 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// <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 virtual void Subtract(Vector other)
+        public virtual Vector Subtract(Vector other)
         {
             if (other == null)
             {
@@ -350,10 +360,12 @@ namespace MathNet.Numerics.LinearAlgebra.Double
                 throw new ArgumentException(Resources.ArgumentVectorsSameLength, "other");
             }
 
+            var copy = this.Clone();
             CommonParallel.For(
                 0, 
                 Count, 
-                index => this[index] -= other[index]);
+                index => copy[index] -= other[index]);
+            return copy;
         }
 
         /// <summary>
@@ -408,17 +420,20 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// <param name="scalar">
         /// The scalar to multiply.
         /// </param>
-        public virtual void Multiply(double scalar)
+        /// <returns>A new vector that is the multiplication of the vector and the scalar.</returns>
+        public virtual Vector Multiply(double scalar)
         {
             if (scalar == 1.0)
             {
-                return;
+                return this.Clone();
             }
 
+            var copy = this.Clone();
             CommonParallel.For(
                 0, 
-                Count, 
-                index => this[index] *= scalar);
+                Count,
+                index => copy[index] *= scalar);
+            return copy;
         }
 
         /// <summary>
@@ -498,14 +513,15 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// <param name="scalar">
         /// The scalar to divide with.
         /// </param>
-        public virtual void Divide(double scalar)
+        /// <returns>A new vector that is the division of the vector and the scalar.</returns>
+        public virtual Vector Divide(double scalar)
         {
             if (scalar == 1.0)
             {
-                return;
+                return this.Clone();
             }
 
-            Multiply(1.0 / scalar);
+            return Multiply(1.0 / scalar);
         }
 
         /// <summary>
@@ -547,9 +563,10 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// Pointwise multiplies this vector with another vector.
         /// </summary>
         /// <param name="other">The vector to pointwise multiply with this one.</param>
+        /// <returns>A new vector which is the pointwise multiplication 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 virtual void PointwiseMultiply(Vector other)
+        public virtual Vector PointwiseMultiply(Vector other)
         {
             if (other == null)
             {
@@ -561,10 +578,12 @@ namespace MathNet.Numerics.LinearAlgebra.Double
                 throw new ArgumentException(Resources.ArgumentVectorsSameLength, "other");
             }
 
+            var copy = this.Clone();
             CommonParallel.For(
                 0, 
-                Count, 
-                index => this[index] *= other[index]);
+                Count,
+                index => copy[index] *= other[index]);
+            return copy;
         }
 
         /// <summary>
@@ -615,9 +634,10 @@ 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 virtual void PointwiseDivide(Vector other)
+        public virtual Vector PointwiseDivide(Vector other)
         {
             if (other == null)
             {
@@ -629,10 +649,12 @@ namespace MathNet.Numerics.LinearAlgebra.Double
                 throw new ArgumentException(Resources.ArgumentVectorsSameLength, "other");
             }
 
+            var copy = this.Clone();
             CommonParallel.For(
                 0, 
                 Count, 
-                index => this[index] /= other[index]);
+                index => copy[index] /= other[index]);
+            return copy;
         }
 
         /// <summary>