How to perform matrix scalar multiplication?

Let’s say A is a matrix with the following elements.

And λ = 3 is a scalar. If we multiply A and λ, we will get another matrix B such that:

In other words, if we multiply a matrix with a scalar, then all the elements of the matrix gets multiplied by the scalar.

How to perform matrix scalar multiplication using Python NumPy?

We can use the following Python code to perform a matrix-scalar multiplication using NumPy.

import numpy

m = 3
n = 4
A = numpy.random.randint(low=1, high=10, size=(m, n))
l = 3
B = l * A

print("A: \n", A)
print("l: ", l)
print("B = l x A: \n", B)

Here, we are first creating an mxn matrix with random integers. We are using the numpy.random.randint() function for that purpose. The generated integers will be within the range [low, high).

The size argument specifies the shape of the matrix. For example, size=(m, n) specifies that the created matrix will have m rows and n columns.

We are them multiplying the generated matrix with a scalar l. The output of the mentioned program will be:

A: 
 [[3 6 1 1]
 [9 2 3 1]
 [8 1 2 5]]
l:  3
B = l x A: 
 [[ 9 18  3  3]
 [27  6  9  3]
 [24  3  6 15]]