Parallel matrix-vector multiplication in NumPy

In this article, we will discuss how to do matrix-vector multiplication in NumPy.

Matrix multiplication with Vector

For a matrix-vector multiplication, there are certain important points:

• The end product of a matrix-vector multiplication is a vector.
• Each element of this vector is obtained by performing a dot product between each row of the matrix and the vector being multiplied.
• The number of columns in the matrix is equal to the number of elements in the vector.

# a and b are matrices
prod = numpy.matmul(a,b)

For matrix-vector multiplication, we will use np.matmul() function of NumPy, we will define a 4 x 4 matrix and a vector of length 4.

Output:

Matrix multiplication with another Matrix

We use the dot product to do matrix-matrix multiplication. We will use the same function for this also.

prod = numpy.matmul(a,b) # a and b are matrices

For a matrix-matrix multiplication, there are certain important points:

• The number of columns in the first matrix should be equal to the number of rows in the second matrix.
• If we are multiplying a matrix of dimensions m x n with another matrix of dimensions n x p, then the resultant product will be a matrix of dimensions m x p

We will define two 3 x 3 matrix:

Output: