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[0]) # 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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