 # Python Program to Find the Sum of all Diagonal Elements of a Matrix

In the previous article, we have discussed Python Program to Check Whether a Matrix is Diagonal or Not

Given a matrix and the task is to find the sum of all diagonal elements of a 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.

Diagonal Matrix:

The entries outside the main diagonal of a diagonal matrix are all 0; the word usually refers to square matrices.

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.

Examples:

Example1:

Input:

Given Matrix :
3 0 0
0 1 0
0 0 2

Output:

The Sum of all Diagonal elements of a given Matix =  6

Example2:

Input:

Given Matrix :
1 2 3
6 5 4
7 8 9

Output:

The Sum of all Diagonal elements of a given Matix = 15

## Program to Find the Sum of all Diagonal Elements of a Matrix in Python

Below are the ways to find the sum of all diagonal elements of a 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 diagnl_sum and initialize its value to zero.
• 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 equal to 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, then add the gvnmatrix[n][m] to the above-initialized diagnl_sum and store it in the same variable diagnl_sum.
• Print the value of diagnl_sum to get the sum of all diagonal elements of a given matrix.
• The Exit of the Program.

Below is the implementation:

# Give the matrix as static input and store it in a variable.
mtrx = [[3, 0, 0], [0, 1, 0], [0, 0, 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)
# Take a variable say diagnl_sum and initialize its value to zero.
diagnl_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 equal to 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, then add the gvnmatrix[n][m] to the above-initialized
# diagnl_sum and store it in the same variable diagnl_sum.
diagnl_sum += mtrx[n][m]
# Print the value of diagnl_sum to get the sum of all diagonal elements of a given matrix.
print("The Sum of all Diagonal elements of a given Matix = ", diagnl_sum)


Output:

The Sum of all Diagonal elements of a given Matix =  6

### 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 say 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 to gvnmatrix using the append() function.
• Take a variable say diagnl_sum and initialize its value to zero.
• 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 equal to 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, then add the gvnmatrix[n][m] to the above-initialized diagnl_sum and store it in the same variable diagnl_sum.
• Print the value of diagnl_sum to get the sum of all diagonal elements of a 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)

# Take a variable say diagnl_sum and initialize its value to zero.
diagnl_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 equal to 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, then add the gvnmatrix[n][m] to the above-initialized
# diagnl_sum and store it in the same variable diagnl_sum.
diagnl_sum += mtrx[n][m]
# Print the value of diagnl_sum to get the sum of all diagonal elements of a given matrix.
print("The Sum of all Diagonal elements of a given Matix = ", diagnl_sum)



Output:

Enter some random number of rows of the matrix = 3
Enter some random number of columns of the matrix = 3
Enter {3} elements of row {1} separated by spaces = 1 2 3
Enter {3} elements of row {2} separated by spaces = 6 5 4
Enter {3} elements of row {3} separated by spaces = 7 8 9
The Sum of all Diagonal elements of a given Matix = 15

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