Program to check diagonal matrix and scalar matrix

Given a square matrix mat[][] of order n*n, the task is to check if it is a Diagonal Matrix and Scalar matrix.

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, 0, 0, 0],
[0, 5, 0, 0],
[0, 0, 2, 0],
[0, 0, 0, 1]]

Output: True
Explanation: Main Diagonal = [4, 5, 2, 1], all the elements except main diagonal are zero.

Input: mat[][] = [[6, 10, 12, 0],
[0, 5, 0, 0],
[0, 0, 9, 0],
[0, 0, 0, 1]]

Output: False
Explanation: Main Diagonal = [6, 5, 9, 1], all the elements except main diagonal are not zero.

Approach:

The row and column indexes of Primary or Major diagonal are same i.e. lets say mat[][] is matrix then mat[i][i] will be a Major Diagonal element. The idea is to traverse the matrix and check if all elements except main diagonal are zero.

// Program to check matrix is diagonal matrix or not.
#include <bits/stdc++.h>
using namespace std;

// Function to check matrix
// is diagonal matrix or not.
bool isDiagonalMatrix(vector<vector<int>> &mat) {
  
    int n = mat.size();
    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;
}

int main() {
    vector<vector<int>> mat = { { 4, 0, 0, 0 },
                      { 0, 7, 0, 0 },
                      { 0, 0, 5, 0 },
                      { 0, 0, 0, 1 } };

    if (isDiagonalMatrix(mat))
        cout << "True" << endl;
    else
        cout << "False" << endl;
    return 0;
}

// Program to check matrix is diagonal matrix or not.
import java.util.*;

class GfG {

    // Function to check matrix
    // is diagonal matrix or not.
    static boolean isDiagonalMatrix(int[][] mat) {
      
        int n = mat.length;
        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;
    }

    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("True");
        else
            System.out.println("False");
    }
}

# Python Program to check if matrix
# is diagonal matrix or not.

# Function to check matrix
# is diagonal matrix or not.

def isDiagonalMatrix(mat):
    n = len(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

mat = [[ 4, 0, 0, 0 ],
       [ 0, 7, 0, 0 ],
       [ 0, 0, 5, 0 ],
       [ 0, 0, 0, 1 ]]

if (isDiagonalMatrix(mat)) :
    print("True")
else :
    print("False")

// C# Program to check if matrix
//  is diagonal matrix or not.
using System;

class GfG {
  
    // Function to check matrix
 	// is diagonal matrix or not.
    static bool isDiagonalMatrix(int [,]mat) {
      
      	int n = mat.GetLength(0);
        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;
    }
    
    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("True");
        else
            Console.WriteLine("False");
    }
}

// JavaScript program to check matrix is
// diagonal matrix or not.

// Function to check matrix
// is diagonal matrix or not.
function isDiagonalMatrix(mat) {

    let n = mat.length;
    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))
    console.log("True");
else
    console.log("False");

True

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.

Scalar Matrix: A square matrix is said to be a scalar matrix if all the main diagonal elements are equal and other elements 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, 0, 0, 0],
[0, 4, 0, 0],
[0, 0, 4, 0],
[0, 0, 0, 4]]

Output: True
Explanation: Main Diagonal = [4, 4, 4, 4] diagonal elements are equal and other elements are zero.

Input: mat[][] = [[4, 0, 0, 0],
[0, 4, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 4]]

Output: False
Explanation: Main Diagonal = [4, 4, 1, 4], diagonal elements are not equal.

Approach:

The row and column indexes of Primary or Major diagonal are same i.e. lets say mat[][] is matrix then mat[i][i] will be a Major Diagonal element. The idea is to traverse the matrix and check if all elements of main diagonal are equal and other elements are zero.

// C++ Program to check matrix is scalar matrix or not.
#include <bits/stdc++.h>
using namespace std;

// Function to check matrix
// is scalar matrix or not.
bool isScalarMatrix(vector<vector<int>> &mat) {
    int n = mat.size();
    for (int i = 0; i < n; i++) {

        // condition to check main diagonal
        // elements are equal or not.
        if((i > 0) && (mat[i][i] != mat[i-1][i-1]))
            return false;

        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;
}

int main() {
    vector<vector<int>> mat = { { 4, 0, 0, 0 },
                      { 0, 4, 0, 0 },
                      { 0, 0, 4, 0 },
                      { 0, 0, 0, 4 } };

    if (isScalarMatrix(mat))
        cout << "True" << endl;
    else
        cout << "False" << endl;
    return 0;
}

// Java Program to check matrix is Scalar matrix or not.
import java.util.*;

class GfG {

    // Function to check matrix
    // is Scalar matrix or not.
    static boolean isScalarMatrix(int[][] mat) {
      
        int n = mat.length;
        for (int i = 0; i < n; i++) {

            // condition to check main diagonal
            // elements are equal or not.
            if((i > 0) && (mat[i][i] != mat[i-1][i-1]))
                return false;

            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;
    }

    public static void main(String[] args) {
        int[][] mat = {
            { 4, 0, 0, 0 },
            { 0, 4, 0, 0 },
            { 0, 0, 4, 0 },
            { 0, 0, 0, 4 }
        };

        if (isScalarMatrix(mat))
            System.out.println("True");
        else
            System.out.println("False");
    }
}

# Python Program to check if matrix
# is Scalar matrix or not.

def isScalarMatrix(mat):
    n = len(mat)
    for i in range(0, n):

        # condition to check main diagonal
        # elements are equal or not.
        if (i > 0) and (mat[i][i] != mat[i - 1][i - 1]):
            return False
        
        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

mat = [[ 4, 0, 0, 0 ],
       [ 0, 4, 0, 0 ],
       [ 0, 0, 4, 0 ],
       [ 0, 0, 0, 4 ]]

if (isScalarMatrix(mat)) :
    print("True")
else :
    print("False")

// C# Program to check matrix is
// Scalar matrix or not.
using System;

class GfG {
  
    // Function to check matrix
 	// is Scalar matrix or not.
    static bool isScalarMatrix(int [,]mat) {
      
      	int n = mat.GetLength(0);
        for (int i = 0; i < n; i++) {

            // condition to check main diagonal
            // elements are equal or not.
            if((i > 0) && (mat[i,i] != mat[i-1,i-1]))
                return false;

            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;
    }
    
    static void Main() {
        int [,]mat = { { 4, 0, 0, 0 },
                        { 0, 4, 0, 0 },
                        { 0, 0, 4, 0 },
                        { 0, 0, 0, 4 } };
    
        if (isScalarMatrix(mat))
            Console.WriteLine("True");
        else
            Console.WriteLine("False");
    }
}

// JavaScript program to check matrix is
// Scalar matrix or not.

// Function to check matrix
// is Scalar matrix or not.
function isScalarMatrix(mat) {

    let n = mat.length;
    for (let i = 0; i < n; i++){

        // condition to check main diagonal
        // elements are equal or not.
        if((i > 0) && (mat[i][i] != mat[i-1][i-1]))
            return false;
        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, 4, 0, 0],
[0, 0, 4, 0],
[0, 0, 0, 4]];

if (isScalarMatrix(mat))
    console.log("True");
else
    console.log("False");

True

Time Complexity: O(n²), where n represents the number of rows and columns of the given matrix.
Auxiliary Space: O(1)