diff --git a/src/Numerics/LinearAlgebra/Double/DenseVector.cs b/src/Numerics/LinearAlgebra/Double/DenseVector.cs
index deae7518..22b1c0df 100644
--- a/src/Numerics/LinearAlgebra/Double/DenseVector.cs
+++ b/src/Numerics/LinearAlgebra/Double/DenseVector.cs
@@ -620,6 +620,38 @@ namespace MathNet.Numerics.LinearAlgebra.Double
             Control.LinearAlgebraProvider.ScaleArray(scalar, Data);
         }
 
+        /// <summary>
+        /// Computes the dot product between this vector and another vector.
+        /// </summary>
+        /// <param name="other">The other vector to add.</param>
+        /// <returns>The result of the addition.</returns>
+        /// <exception cref="ArgumentException">If <paramref name="other"/> is not of the same size.</exception>
+        /// <exception cref="ArgumentNullException">If <paramref name="other"/> is <see langword="null" />.</exception>
+        public override double DotProduct(Vector other)
+        {
+            if (other == null)
+            {
+                throw new ArgumentNullException("other");
+            }
+
+            if (Count != other.Count)
+            {
+                throw new ArgumentException(Resources.ArgumentVectorsSameLength, "other");
+            }
+
+
+            var denseVector = other as DenseVector;
+
+            if (denseVector == null)
+            {
+                return base.DotProduct(other);
+            }
+            else
+            {
+                return Control.LinearAlgebraProvider.DotProduct(this.Data, denseVector.Data);
+            }
+        }
+
         /// <summary>
         /// Multiplies a vector with a scalar.
         /// </summary>
@@ -658,6 +690,34 @@ namespace MathNet.Numerics.LinearAlgebra.Double
             return ret;
         }
 
+        /// <summary>
+        /// Computes the dot product between two <strong>Vectors</strong>.
+        /// </summary>
+        /// <param name="leftSide">The left row vector.</param>
+        /// <param name="rightSide">The right column vector.</param>
+        /// <returns>The dot product between the two vectors.</returns>
+        /// <exception cref="ArgumentException">If <paramref name="leftSide"/> and <paramref name="rightSide"/> are not the same size.</exception>
+        /// <exception cref="ArgumentNullException">If <paramref name="leftSide"/> or <paramref name="rightSide"/> is <see langword="null" />.</exception>
+        public static double operator *(DenseVector leftSide, DenseVector rightSide)
+        {
+            if (rightSide == null)
+            {
+                throw new ArgumentNullException("rightSide");
+            }
+
+            if (leftSide == null)
+            {
+                throw new ArgumentNullException("leftSide");
+            }
+
+            if (leftSide.Count != rightSide.Count)
+            {
+                throw new ArgumentException(Resources.ArgumentVectorsSameLength, "rightSide");
+            }
+
+            return Control.LinearAlgebraProvider.DotProduct(leftSide.Data, rightSide.Data);
+        }
+
         /// <summary>
         /// Divides a vector with a scalar.
         /// </summary>
diff --git a/src/Numerics/LinearAlgebra/Double/Vector.cs b/src/Numerics/LinearAlgebra/Double/Vector.cs
index 58e61b51..88dabe95 100644
--- a/src/Numerics/LinearAlgebra/Double/Vector.cs
+++ b/src/Numerics/LinearAlgebra/Double/Vector.cs
@@ -370,6 +370,34 @@ namespace MathNet.Numerics.LinearAlgebra.Double
             result.Multiply(scalar);
         }
 
+        /// <summary>
+        /// Computes the dot product between this vector and another vector.
+        /// </summary>
+        /// <param name="other">The other vector to add.</param>
+        /// <returns>The result of the addition.</returns>
+        /// <exception cref="ArgumentException">If <paramref name="other"/> is not of the same size.</exception>
+        /// <exception cref="ArgumentNullException">If <paramref name="other"/> is <see langword="null" />.</exception>
+        public virtual double DotProduct(Vector other)
+        {
+            if (other == null)
+            {
+                throw new ArgumentNullException("other");
+            }
+
+            if (Count != other.Count)
+            {
+                throw new ArgumentException(Resources.ArgumentVectorsSameLength, "other");
+            }
+
+            double dot = 0.0;
+            for (int i = 0; i < Count; i++)
+            {
+                dot += this[i] * other[i];
+            }
+
+            return dot;
+        }
+
         /// <summary>
         /// Divides each element of the vector by a scalar.
         /// </summary>
@@ -544,6 +572,34 @@ namespace MathNet.Numerics.LinearAlgebra.Double
             return ret;
         }
 
+        /// <summary>
+        /// Computes the dot product between two <strong>Vectors</strong>.
+        /// </summary>
+        /// <param name="leftSide">The left row vector.</param>
+        /// <param name="rightSide">The right column vector.</param>
+        /// <returns>The dot product between the two vectors.</returns>
+        /// <exception cref="ArgumentException">If <paramref name="leftSide"/> and <paramref name="rightSide"/> are not the same size.</exception>
+        /// <exception cref="ArgumentNullException">If <paramref name="leftSide"/> or <paramref name="rightSide"/> is <see langword="null" />.</exception>
+        public static double operator *(Vector leftSide, Vector rightSide)
+        {
+            if (rightSide == null)
+            {
+                throw new ArgumentNullException("rightSide");
+            }
+
+            if (leftSide == null)
+            {
+                throw new ArgumentNullException("leftSide");
+            }
+
+            if (leftSide.Count != rightSide.Count)
+            {
+                throw new ArgumentException(Resources.ArgumentVectorsSameLength, "rightSide");
+            }
+
+            return leftSide.DotProduct(rightSide);
+        }
+
         /// <summary>
         /// Divides a vector with a scalar.
         /// </summary>
diff --git a/src/UnitTests/LinearAlgebraTests/Double/VectorTests.Arithmetic.cs b/src/UnitTests/LinearAlgebraTests/Double/VectorTests.Arithmetic.cs
index a1bf8118..54c36b88 100644
--- a/src/UnitTests/LinearAlgebraTests/Double/VectorTests.Arithmetic.cs
+++ b/src/UnitTests/LinearAlgebraTests/Double/VectorTests.Arithmetic.cs
@@ -628,5 +628,73 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double
             Vector vector = null;
             Assert.Throws<ArgumentNullException>(() => vector = vector / 2.0);
         }
+
+        [Test]
+        public void CanDotProduct()
+        {
+            Vector dataA = CreateVector(_data);
+            Vector dataB = CreateVector(_data);
+
+            Assert.AreEqual(55.0, dataA.DotProduct(dataB));
+        }
+
+        [Test]
+        [ExpectedArgumentNullException]
+        public void DotProductThrowsExceptionWhenArgumentIsNull()
+        {
+            Vector dataA = CreateVector(_data);
+            Vector dataB = null;
+
+            dataA.DotProduct(dataB);
+        }
+
+        [Test]
+        [ExpectedArgumentException]
+        public void DotProductThrowsExceptionWhenArgumentHasDifferentSize()
+        {
+            Vector dataA = CreateVector(_data);
+            Vector dataB = CreateVector(new double[] {1, 2, 3, 4, 5, 6});
+
+            dataA.DotProduct(dataB);
+        }
+
+        [Test]
+        public void CanDotProductUsingOperator()
+        {
+            Vector dataA = CreateVector(_data);
+            Vector dataB = CreateVector(_data);
+
+            Assert.AreEqual(55.0, dataA * dataB);
+        }
+
+        [Test]
+        [ExpectedArgumentNullException]
+        public void OperatorDotProductThrowsExceptionWhenLeftArgumentIsNull()
+        {
+            Vector dataA = CreateVector(_data);
+            Vector dataB = null;
+
+            double d = dataA * dataB;
+        }
+
+        [Test]
+        [ExpectedArgumentNullException]
+        public void OperatorDotProductThrowsExceptionWhenRightArgumentIsNull()
+        {
+            Vector dataA = null;
+            Vector dataB = CreateVector(_data);
+
+            double d = dataA * dataB;
+        }
+
+        [Test]
+        [ExpectedArgumentException]
+        public void OperatorDotProductThrowsExceptionWhenArgumentHasDifferentSize()
+        {
+            Vector dataA = CreateVector(_data);
+            Vector dataB = CreateVector(new double[] { 1, 2, 3, 4, 5, 6 });
+
+            double d = dataA * dataB;
+        }
     }
 }
\ No newline at end of file