# Python Program to Find the Sum of a Lower Triangular Matrix

In the previous article, we have discussed Python Program to Find the Sum of an Upper Triangular Matrix

Given a matrix and the task is to find the sum of the lower triangular matrix of the given matrix in Python.

What is a matrix:

A matrix is a rectangular sequence of numbers divided into columns and rows. A matrix element or entry is a number that appears in a matrix.

Example:

Above is the matrix which contains 5 rows and 4 columns and having elements from 1 to 20.

In this order, the dimensions of a matrix indicate the number of rows and columns.

Here as there are 5 rows and 4 columns it is called a 5*4 matrix.

Lower Triangular Matrix:

A lower triangular matrix is one that has all of its upper triangular elements equal to zero. In other words, all non-zero elements are on the main diagonal or in the lower triangle.

Examples:

Example1:

Input:

Given Matix :
1 6 4
8 1 3
1 6 2

Output:

The sum of Lower Triangular matrix of the given matrix is :
13

Example2:

Input:

Given Matix :
7 9
3 6

Output:

The sum of Lower Triangular matrix of the given matrix is :
9

## Program to Find the Sum of a Lower Triangular Matrix in Python

Below are the ways to find the sum of the lower triangular matrix of the given matrix in Python.

### Method #1: Using For Loop (Static Input)

Approach:

• Give the matrix as static input and store it in a variable.
• Calculate the number of rows of the given matrix by calculating the length of the nested list using the len() function and store it in a variable mtrxrows.
• Calculate the number of columns of the given matrix by calculating the length of the first list in the nested list using the len() function and store it in a variable mtrxcolums.
• Take a variable say lower_sum and initialize its value to 0.
• Loop till the given number of rows using the For loop.
• Inside the For loop, Iterate till the given number of columns using another Nested For loop(Inner For loop).
• Check if the condition n is less than m using the if conditional statement where n is the iterator value of the parent For loop and m is the iterator value of the inner For loop.
• If the statement is true, add the gvnmatrix[n][m] to the above-initialized lower_sumÂ and store it in the same variable lower_sum.
• Print the variable lower_sumÂ to get the sum of the lower triangular matrix of the given matrix.
• The Exit of the Program.

Below is the implementation:

# Give the matrix as static input and store it in a variable.
mtrx = [[1, 6, 4], [8, 1, 3], [1, 6, 2]]
# Calculate the number of rows of the given matrix by
# calculating the length of the nested list using the len() function
# and store it in a variable mtrxrows.
mtrxrows = len(mtrx)
# Calculate the number of columns of the given matrix by
# calculating the length of the first list in the nested list
# using the len() function and store it in a variable mtrxcols.
mtrxcols = len(mtrx[0])
print("The sum of Lower Triangular matrix of the given matrix is :")
# Take a variable say lower_sum and initialize its value to 0.
lower_sum = 0
# To print all the elements of the given matrix.
# Loop till the given number of rows using the For loop.
for n in range(mtrxrows):
# Inside the For loop, Iterate till the given number of columns using another
# Nested For loop(Inner For loop).
for m in range(mtrxcols):
# Check if the condition n is less than m using the if conditional statement where n
# is the iterator value of the parent For loop and m is the iterator value of the
# inner For loop.
if n < m:
# If the statement is true, add the gvnmatrix[n][m] to the above-initialized
# lower_sumÂ and store it in the same variable lower_sum.
lower_sum += mtrx[n][m]
# Print the variable lower_sumÂ to get the sum of the lower triangular matrix of the
# given matrix.
print(lower_sum)


Output:

The sum of Lower Triangular matrix of the given matrix is :
13

### Method #2: Using For loop (User Input)

Approach:

• Give the number of rows of the matrix as user input using the int(input()) function and store it in a variable.
• Give the number of columns of the matrix as user input using the int(input()) function and store it in another variable.
• Take a list and initialize it with an empty value using [] or list() to sayÂ gvnmatrix.
• Loop till the given number of rows using the For loop
• Inside the For loop, Give all the row elements of the given Matrix as a list using the list(),map(),int(),split() functions and store it in a variable.
• Add the above row elements list toÂ gvnmatrixÂ using the append() function.
• Take a variable say lower_sum and initialize its value to 0.
• Loop till the given number of rows using the For loop.
• Inside the For loop, Iterate till the given number of columns using another Nested For loop(Inner For loop).
• Check if the condition n is less than m using the if conditional statement where n is the iterator value of the parent For loop and m is the iterator value of the inner For loop.
• If the statement is true, add the gvnmatrix[n][m] to the above-initialized lower_sumÂ and store it in the same variable lower_sum.
• Print the variable lower_sumÂ to get the sum of the lower triangular matrix of the given matrix.
• The Exit of the Program.

Below is the implementation:

# Give the number of rows of the matrix as user input using the int(input()) function
# and store it in a variable.
mtrxrows = int(input('Enter some random number of rows of the matrix = '))
# Give the number of columns of the matrix as user input using the int(input()) function
# and store it in another variable.
mtrxcols = int(input('Enter some random number of columns of the matrix = '))
# Take a list and initialize it with an empty value using [] or list() to say gvnmatrix.
mtrx = []
# Loop till the given number of rows using the For loop
for n in range(mtrxrows):
# Inside the For loop, Give all the row elements of the given Matrix as a list using
# the list(),map(),int(),split() functions and store it in a variable.
l = list(map(int, input(
'Enter {'+str(mtrxcols)+'} elements of row {'+str(n+1)+'} separated by spaces = ').split()))
# Add the above row elements list to gvnmatrix using the append() function.

mtrx.append(l)

print("The sum of Lower Triangular matrix of the given matrix is :")
# Take a variable say lower_sum and initialize its value to 0.
lower_sum = 0
# To print all the elements of the given matrix.
# Loop till the given number of rows using the For loop.
for n in range(mtrxrows):
# Inside the For loop, Iterate till the given number of columns using another
# Nested For loop(Inner For loop).
for m in range(mtrxcols):
# Check if the condition n is less than m using the if conditional statement where n
# is the iterator value of the parent For loop and m is the iterator value of the
# inner For loop.
if n < m:
# If the statement is true, add the gvnmatrix[n][m] to the above-initialized
# lower_sumÂ and store it in the same variable lower_sum.
lower_sum += mtrx[n][m]
# Print the variable lower_sumÂ to get the sum of the lower triangular matrix of the
# given matrix.
print(lower_sum)


Output:

Enter some random number of rows of the matrix = 2
Enter some random number of columns of the matrix = 2
Enter {2} elements of row {1} separated by spaces = 7 9
Enter {2} elements of row {2} separated by spaces = 3 6
The sum of Lower Triangular matrix of the given matrix is :
9

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