What is a lower triangular matrix?

A lower triangular matrix is a square matrix in which all the elements above the principal diagonal are zero. For example, the matrix A given below is a lower triangular matrix.

So, if a_i,j is the element in the ith row and jth column of the matrix A, then we can say that the square matrix A is a lower triangular matrix if the following condition holds true:

So, the square matrix B given below is a 3×3 lower triangular matrix.

How to create a lower triangular matrix using Python NumPy?

We can use the following Python code to create a lower triangular matrix using NumPy.

import numpy

n = 3
A = numpy.random.randint(low=1, high=10, size=(n, n))

L = numpy.tril(A, k=0)
print("A: \n", A)
print("The Lower Triangular Matrix L: \n", L)

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