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.
Python3
import numpy as np a = np.array([[1, 2, 3, 13], [4, 5, 6, 14], [7, 8, 9, 15], [10, 11, 12, 16]]) b = np.array([10, 20, 30, 40]) print("Matrix a =", a) print("Matrix b =", b) print("Product of a and b =", np.matmul(a, b)) |
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:
Python3
import numpy as np a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) b = np.array([[11, 22, 33], [44, 55, 66], [77, 88, 99]]) print("Matrix a =", a) print("Matrix b =", b) print("Product of a and b =", np.matmul(a, b)) |
Output:
