# Python Program to Find the Sum of an Upper Triangular Matrix

In the previous article, we have discussed Python Program to Find the Sum of all Elements in a 2D Array

Given a matrix and the task is to find the sum of an upper 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.

Upper Triangular Matrix:

An upper triangular matrix is a square matrix in which all of the entries below the major diagonal are zero.

Examples:

Example1:

Input:

Given Matrix :
6 2 1
1 5 0
2 8 3

Output:

The sum of Upper Triangular matrix of the given matrix is :
11

Example2:

Input:

Given Matrix :
4 3
9 8

Output:

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

## Program to Find the Sum of an Upper Triangular Matrix in Python

Below are the ways to find the sum of an upper 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 uppr_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 greater 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 uppr_sum and store it in the same variable uppr_sum.
• Print the variable uppr_sum to get the sum of an upper 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 = [[6, 2, 1], [1, 5, 0], [2, 8, 3]]
# 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 Upper Triangular matrix of the given matrix is :")
# Take a variable say uppr_sum and initialize its value to 0.
uppr_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 greater 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
# uppr_sum and store it in the same variable uppr_sum.
uppr_sum += mtrx[n][m]
# Print the variable uppr_sum to get the sum of an upper triangular matrix of the
# given matrix.
print(uppr_sum)


Output:

The sum of Upper Triangular matrix of the given matrix is :
11

### 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 uppr_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 greater 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 uppr_sum and store it in the same variable uppr_sum.
• Print the variable uppr_sum to get the sum of an upper 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)

# Take a variable say uppr_sum and initialize its value to 0.
uppr_sum = 0
print("The sum of Upper Triangular matrix of the given matrix is :")
# 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 greater 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
# uppr_sum and store it in the same variable uppr_sum.
uppr_sum += mtrx[n][m]
# Print the variable uppr_sum to get the sum of an upper triangular matrix of the
# given matrix.
print(uppr_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 = 4 3
Enter {2} elements of row {2} separated by spaces = 9 8
The sum of Upper Triangular matrix of the given matrix is :
9

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