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
**gvnmatrix**Â 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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