In the previous article, we have discussed Python Program to Check if a Pair with Given Product Exists in a Matrix

Given a square matrix and the task is to check whether the given matrix is a diagonally dominant matrix or not.

**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.

**Diagonally Dominant Matrix :**

A square matrix is said to be diagonally dominating in mathematics if the magnitude of the diagonal entry in a row is greater than or equal to the sum of the magnitudes of all the other (non-diagonal) values in that row for each row of the matrix.

**Examples:**

**Example1:**

**Input:**

Given Matrix : 5 1 3 2 7 1 4 0 9

**Output:**

Yes, the given matrix is a diagonally dominant matrix

**Example2:**

**Input:**

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

**Output:**

No, the given matrix is not a diagonally dominant matrix

## Program to Check Diagonally Dominant Matrix in Python

Below are the ways to check whether the given matrix is a diagonally dominant matrix or not 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.
- Create a function to say
**checkdiagnolydominant_matx()**which takes the given matrix and the number of rows of the given matrix as the arguments and returns true or false. - Inside the function,Â Loop till the given number of rows using the For loop.
- Take a variable to say
**rslt_summÂ**and initialize its value to 0. -
Inside the For loop, Iterate till the given number of rows using another Nested For loop(Inner For loop).
- Add the absolute of mtrx[n][m] to the above-initializedÂ rslt_summ and store it in the same variable.
- Remove the diagonal element by subtracting the abs(mtrx[n][n]) from the
**rslt_summ**and store it in the same variable. - Check if the abs(mtrx[n][n]) (diagonal element) is less than the
**rslt_summ**(Which is the sum of non diagonal elements) using the if conditional statement. - If it is true, then return False.
- Return True.
- Pass the given matrix and the number of rows of the given matrix as the arguments to the
**checkdiagnolydominant_matx()**function and check if returns true or false using the if conditional statement. - If it is true, print “Yes, the given matrix is a diagonally dominant matrix”.
- Else print “No, the given matrix is not a diagonally dominant matrix”.
- The Exit of the Program.

**Below is the implementation:**

# Create a function to say checkdiagnolydominant_matx() which takes the given matrix # and the number of rows of the given matrix as the arguments and returns true or false def checkdiagnolydominant_matx(mtrx, mtrxrows): # Inside the function,Â Loop till the given number of rows using the For loop. for n in range(0, mtrxrows): # Take a variable to say rslt_summÂ and initialize its value to 0. rslt_summ = 0 # Inside the For loop, Iterate till the given number of rows using another # Nested For loop(Inner For loop). for m in range(0, mtrxrows): # Add the absolute of mtrx[n][m] to the above-initializedÂ rslt_summ and store # it in the same variable. rslt_summ = rslt_summ + abs(mtrx[n][m]) # Remove the diagonal element by subtracting the abs(mtrx[n][n]) from the rslt_summ and # store it in the same variable. rslt_summ = rslt_summ - abs(mtrx[n][n]) # Check if the abs(mtrx[n][n]) (diagonal element) is less than the rslt_summ # (Which is the #sum of non diagonal elements) using the if conditional statement. if (abs(mtrx[n][n]) < rslt_summ): # If it is true, then return False. return False # Return True. return True # Give the matrix as static input and store it in a variable. mtrx = [[5, 1, 3], [2, 7, 1], [4, 0, 9]] # 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]) # Pass the given matrix and the number of rows of the given matrix as the arguments # to the checkdiagnolydominant_matx() function and check if returns true or false # using the if conditional statement. if((checkdiagnolydominant_matx(mtrx, mtrxrows))): # If it is true, print "Yes, the given matrix is a diagonally dominant matrix". print("Yes, the given matrix is a diagonally dominant matrix") else: # Else print "No, the given matrix is not a diagonally dominant matrix". print("No, the given matrix is not a diagonally dominant matrix")

**Output:**

Yes, the given matrix is a diagonally dominant matrix

### 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. - Create a function to say
**checkdiagnolydominant_matx()**which takes the given matrix and the number of rows of the given matrix as the arguments and returns true or false. - Inside the function,Â Loop till the given number of rows using the For loop.
- Take a variable to say
**rslt_summÂ**and initialize its value to 0. -
Inside the For loop, Iterate till the given number of rows using another Nested For loop(Inner For loop).
- Add the absolute of mtrx[n][m] to the above-initializedÂ rslt_summ and store it in the same variable.
- Remove the diagonal element by subtracting the abs(mtrx[n][n]) from the
**rslt_summ**and store it in the same variable. - Check if the abs(mtrx[n][n]) (diagonal element) is less than the
**rslt_summ**(Which is the sum of non diagonal elements) using the if conditional statement. - If it is true, then return False.
- Return True.
- Pass the given matrix and the number of rows of the given matrix as the arguments to the
**checkdiagnolydominant_matx()**function and check if returns true or false using the if conditional statement. - If it is true, print “Yes, the given matrix is a diagonally dominant matrix”.
- Else print “No, the given matrix is not a diagonally dominant matrix”.
- The Exit of the Program.

**Below is the implementation:**

# Create a function to say checkdiagnolydominant_matx() which takes the given matrix # and the number of rows of the given matrix as the arguments and returns true or false def checkdiagnolydominant_matx(mtrx, mtrxrows): # Inside the function,Â Loop till the given number of rows using the For loop. for n in range(0, mtrxrows): # Take a variable to say rslt_summÂ and initialize its value to 0. rslt_summ = 0 # Inside the For loop, Iterate till the given number of rows using another # Nested For loop(Inner For loop). for m in range(0, mtrxrows): # Add the absolute of mtrx[n][m] to the above-initializedÂ rslt_summ and store # it in the same variable. rslt_summ = rslt_summ + abs(mtrx[n][m]) # Remove the diagonal element by subtracting the abs(mtrx[n][n]) from the rslt_summ and # store it in the same variable. rslt_summ = rslt_summ - abs(mtrx[n][n]) # Check if the abs(mtrx[n][n]) (diagonal element) is less than the rslt_summ # (Which is the #sum of non diagonal elements) using the if conditional statement. if (abs(mtrx[n][n]) < rslt_summ): # If it is true, then return False. return False # Return True. return True # 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) if((checkdiagnolydominant_matx(mtrx, mtrxrows))): # If it is true, print "Yes, the given matrix is a diagonally dominant matrix". print("Yes, the given matrix is a diagonally dominant matrix") else: # Else print "No, the given matrix is not a diagonally dominant matrix". print("No, the given matrix is not a diagonally dominant matrix")

**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 3 5 Enter {3} elements of row {2} separated by spaces = 2 4 6 Enter {3} elements of row {3} separated by spaces = 7 8 9 No, the given matrix is not a diagonally dominant matrix

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