Program to check diagonal matrix and scalar matrix

Read

Discuss

Diagonal matrix

A square matrix is said to be a diagonal matrix if the elements of the matrix except the main diagonal are zero. A square null matrix is also a diagonal matrix whose main diagonal elements are zero.

Examples:

Input: 
Mat[4][4] = {{4, 0, 0, 0},
             {0, 5, 0, 0},
             {0, 0, 2, 0},
             {0, 0, 0, 1}}
Output: Yes

Input:
Mat[4][4] = {{6, 10, 12, 0},
             {0, 5, 0, 0},
             {0, 0, 9, 0},
             {0, 0, 0, 1}}
Output: No

Below is the implementation:

CPP

// Program to check matrix is diagonal matrix or not.
 
#include <bits/stdc++.h>
#define N 4
using namespace std;
 
// Function to check matrix
// is diagonal matrix or not.
bool isDiagonalMatrix(int mat[N][N])
{
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
 
            // condition to check other elements 
            // except main diagonal are zero or not.
            if ((i != j) && (mat[i][j] != 0))
                return false;
    return true;
}
 
// Driver function
int main()
{
    int mat[N][N] = { { 4, 0, 0, 0 },
                      { 0, 7, 0, 0 },
                      { 0, 0, 5, 0 },
                      { 0, 0, 0, 1 } };
 
    if (isDiagonalMatrix(mat))
        cout << "Yes" << endl;
    else
        cout << "No" << endl;
    return 0;
}

Java

// Program to check matrix is
// diagonal matrix or not.
 
import java.io.*;
 
class GFG {
     
    static int N = 4;
     
    // Function to check matrix
    // is diagonal matrix
    // or not.
    static boolean isDiagonalMatrix(int mat[][])
    {
        for (int i = 0; i < N; i++)
            for (int j = 0; j < N; j++)
      
                // condition to check
                // other elements 
                // except main diagonal 
                // are zero or not.
                if ((i != j) &&
                   (mat[i][j] != 0))
                    return false;
 
        return true;
    }
      
    // Driver function
    public static void main(String args[])
    {
        int mat[][] = { { 4, 0, 0, 0 },
                          { 0, 7, 0, 0 },
                          { 0, 0, 5, 0 },
                          { 0, 0, 0, 1 } };
      
        if (isDiagonalMatrix(mat))
            System.out.println("Yes");
        else
            System.out.println("No" );
    }
}
 
// This code is contributed by
// Nikita Tiwari.

Python3

# Python3 Program to check if matrix
# is diagonal matrix or not.
 
N = 4
 
# Function to check matrix
# is diagonal matrix
# or not.   
def isDiagonalMatrix(mat) :
    for i in range(0, N):
        for j in range(0, N) :
             
            # condition to check
            # other elements 
            # except main diagonal
            # are zero or not.
            if ((i != j) and
             (mat[i][j] != 0)) :
                return False
 
    return True
 
 
# Driver function
mat = [[ 4, 0, 0, 0 ],
       [ 0, 7, 0, 0 ],
       [ 0, 0, 5, 0 ],
       [ 0, 0, 0, 1 ]]
 
if (isDiagonalMatrix(mat)) :
    print("Yes")
else :
    print("No")
     
     
# This code is contributed by Nikita Tiwari.

C#

// Program to check matrix is
// diagonal matrix or not.
using System;
 
class GFG {
     
    static int N = 4;
     
    // Function to check matrix
    // is diagonal matrix
    // or not.
    static bool isDiagonalMatrix(int [,]mat)
    {
        for (int i = 0; i < N; i++)
            for (int j = 0; j < N; j++)
     
                // condition to check
                // other elements 
                // except main diagonal 
                // are zero or not.
                if ((i != j) &&    (mat[i,j] != 0))
                    return false;
 
        return true;
    }
     
    // Driver function
    public static void Main()
    {
        int [,]mat = { { 4, 0, 0, 0 },
                        { 0, 7, 0, 0 },
                        { 0, 0, 5, 0 },
                        { 0, 0, 0, 1 } };
     
        if (isDiagonalMatrix(mat))
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No" );
    }
}
 
// This code is contributed by
// vt_m.

PHP

<?php
// Program to check matrix is
// diagonal matrix or not.
 
$N= 4;
 
// Function to check matrix is
// diagonal matrix or not.
function isDiagonalMatrix($mat)
{
    global $N;
    for ($i = 0; $i < $N; $i++)
        for ($j = 0; $j < $N; $j++)
 
            // condition to check
            // other elements 
            // except main diagonal
            // are zero or not.
            if (($i != $j) && 
                ($mat[$i][$j] != 0))
                return false;
    return true;
}
 
    // Driver Code
    $mat = array(array(4, 0, 0, 0),
                 array(0, 7, 0, 0),
                 array(0, 0, 5, 0),
                 array(0, 0, 0, 1));
 
    if (isDiagonalMatrix($mat))
        echo "Yes" ,"\n";
    else
        echo "No","\n";
 
// This code is contributed by jit_t
?>

Javascript

<script>
 
// JavaScript program to check matrix is
// diagonal matrix or not.
 
let N = 4;
       
    // Function to check matrix
    // is diagonal matrix
    // or not.
    function isDiagonalMatrix(mat)
    {
        for (let i = 0; i < N; i++)
            for (let j = 0; j < N; j++)
        
                // condition to check
                // other elements 
                // except main diagonal 
                // are zero or not.
                if ((i != j) &&
                   (mat[i][j] != 0))
                    return false;
   
        return true;
    }
 
// Driver code
 
        let mat = [[ 4, 0, 0, 0 ],
                          [ 0, 7, 0, 0 ],
                          [ 0, 0, 5, 0 ],
                          [ 0, 0, 0, 1 ]];
        
        if (isDiagonalMatrix(mat))
            document.write("Yes");
        else
            document.write("No" );
 
</script>

Output

Yes

Time Complexity: O(N²), where N represents the number of rows and columns of the given matrix.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

Scalar matrix

A square matrix is said to be a scalar matrix if all the main diagonal elements are equal and other elements except main diagonal are zero. The scalar matrix can also be written in form of n * I, where n is any real number and I is the identity matrix.

Examples:

Input:
Mat[4][4] = {{4, 0, 0, 0},
             {0, 4, 0, 0},
             {0, 0, 4, 0},
             {0, 0, 0, 4}} 
Output: Yes

Input:
Mat[4][4] = {{4, 0, 0, 0},
             {0, 4, 0, 0},
             {0, 0, 1, 0},
             {0, 0, 0, 4}} 
Output: No

Below is the implementation:

CPP

// Program to check matrix is scalar matrix or not.
#include <bits/stdc++.h>
#define N 4
using namespace std;
 
// Function to check matrix is scalar matrix or not.
bool isScalarMatrix(int mat[N][N])
{
    // Check all elements except main diagonal are
    // zero or not.
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            if ((i != j) && (mat[i][j] != 0))
                return false;
 
    // Check all diagonal elements are same or not.
    for (int i = 0; i < N - 1; i++)
        if (mat[i][i] != mat[i + 1][i + 1])
            return false;
    return true;
}
 
// Driver function
int main()
{
    int mat[N][N] = { { 2, 0, 0, 0 },
                      { 0, 2, 0, 0 },
                      { 0, 0, 2, 0 },
                      { 0, 0, 0, 2 } };
    // Function call
    if (isScalarMatrix(mat))
        cout << "Yes" << endl;
    else
        cout << "No" << endl;
    return 0;
}

Java

// Program to check matrix
// is scalar matrix or not.
import java.io.*;
 
class GFG {
     
    static int N = 4;
    // Function to check matrix
    // is scalar matrix or not.
    static boolean isScalarMatrix(int mat[][])
    {
        // Check all elements
        // except main diagonal are
        // zero or not.
        for (int i = 0; i < N; i++)
            for (int j = 0; j < N; j++)
                if ((i != j)
                  && (mat[i][j] != 0))
                    return false;
      
        // Check all diagonal elements
        // are same or not.
        for (int i = 0; i < N - 1; i++)
            if (mat[i][i] != mat[i + 1][i + 1])
                return false;
        return true;
    }
      
    // Driver function
    public static void main(String args[])
    {
        int mat[ ][ ] = { { 2, 0, 0, 0 },
                          { 0, 2, 0, 0 },
                          { 0, 0, 2, 0 },
                          { 0, 0, 0, 2 } };
        // Function call
        if (isScalarMatrix(mat))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}
 
// This code is contributed
// by Nikita tiwari.

Python3

# Program to check matrix
# is scalar matrix or not.
 
 
N = 4
 
# Function to check matrix is
# scalar matrix or not.
def isScalarMatrix(mat) :
     
    # Check all elements 
    # except main diagonal are
    # zero or not.
    for i in range(0,N) :
        for j in range(0,N) :
            if ((i != j) 
               and (mat[i][j] != 0)) :
                return False
  
    # Check all diagonal
    # elements are same or not.
    for i in range(0,N-1) :
        if (mat[i][i] !=
           mat[i + 1][i + 1]) :
            return False
 
    return True
 
 
# Driver function
mat = [[ 2, 0, 0, 0 ],
       [ 0, 2, 0, 0 ],
       [ 0, 0, 2, 0 ],
       [ 0, 0, 0, 2 ]]
 
# Function call
if (isScalarMatrix(mat)):
    print("Yes")
else :
    print("No")
     
     
# This code is contributed by
# Nikita tiwari.

C#

// Program to check matrix
// is scalar matrix or not.
using System;
 
class GFG {
     
    static int N = 4;
     
    // Function to check matrix
    // is scalar matrix or not.
    static bool isScalarMatrix(int [,]mat)
    {
        // Check all elements
        // except main diagonal are
        // zero or not.
        for (int i = 0; i < N; i++)
            for (int j = 0; j < N; j++)
                if ((i != j) && (mat[i,j] != 0))
                    return false;
     
        // Check all diagonal elements
        // are same or not.
        for (int i = 0; i < N - 1; i++)
            if (mat[i, i] != mat[i + 1, i + 1])
                return false;
        return true;
    }
     
    // Driver function
    public static void Main()
    {
        int [,]mat = { { 2, 0, 0, 0 },
                        { 0, 2, 0, 0 },
                        { 0, 0, 2, 0 },
                        { 0, 0, 0, 2 } };
        // Function call
        if (isScalarMatrix(mat))
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
    }
}
 
// This code is contributed
// by vt_m.

PHP

<?php
// Program to check matrix
// is scalar matrix or not.
 
$N = 4;
 
// Function to check matrix 
// is scalar matrix or not.
function isScalarMatrix($mat)
{
    global $N;
    // Check all elements except 
    // main diagonal are zero or not.
    for ($i = 0; $i < $N; $i++)
        for ($j = 0; $j < $N; $j++)
            if (($i != $j) &&
                ($mat[$i][$j] != 0))
                return false;
 
    // Check all diagonal elements 
    // are same or not.
    for ($i = 0; $i < $N - 1; $i++)
        if ($mat[$i][$i] != $mat[$i + 1][$i + 1])
            return false;
    return true;
}
 
// Driver Code
$mat = array(array(2, 0, 0, 0),
             array(0, 2, 0, 0),
             array(0, 0, 2, 0),
             array(0, 0, 0, 2));
              
// Function call
if (isScalarMatrix($mat))
    echo "Yes";
else
    echo "No" ;
 
// This code is contributed by mits
?>

Javascript

<script>
// Javascript Program to check matrix
// is scalar matrix or not. 
   let N = 4;
    
    // Function to check matrix
    // is scalar matrix or not.
    function isScalarMatrix(mat)
    {
     
        // Check all elements
        // except main diagonal are
        // zero or not.
        for (let i = 0; i < N; i++)
            for (let j = 0; j < N; j++)
                if ((i != j)
                  && (mat[i][j] != 0))
                    return false;
       
        // Check all diagonal elements
        // are same or not.
        for (let i = 0; i < N - 1; i++)
            if (mat[i][i] != mat[i + 1][i + 1])
                return false;
        return true;
    }
      
 
    // Driver Code
    let mat = [[ 2, 0, 0, 0 ],
                          [ 0, 2, 0, 0 ],
                          [ 0, 0, 2, 0 ],
                          [ 0, 0, 0, 2 ]];
                           
        // Function call
        if (isScalarMatrix(mat))
            document.write("Yes");
        else
            document.write("No");
 
// This code is contributed by souravghosh0416.
</script>

Output

Yes

Time Complexity: O(N²), where N represents the number of rows and columns of the given matrix.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

Recommended

Solve DSA problems on GfG Practice.

Solve Problems

Feeling lost in the world of random DSA topics, wasting time without progress? It's time for a change! Join our DSA course, where we'll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 geeks!

Last Updated : 01 Aug, 2022