Check Diagonal Matrix and Scalar Matrix

Program Explanation

1. The number of rows and columns must be entered by the user.

2. If not, the elements are instructed to input and save data in the matrix.

3. The matrix's diagonal members are examined. If they're both 0, a temporary variable called 'p' is set to 1.

4. If none of the non-diagonal components are 0, p is given a value of 1.

5. If the flag is set to 1, the inputted array is not a diagonal matrix; otherwise, it is.

6. Finally, the result is printed.

Scalar Matrix

A scalar matrix is a square matrix. If all of the major diagonal elements are equal and all other members except the main diagonal are zero. The identity matrix is expressed as n * I, where n is any real number, and I is the scalar matrix.

Algorithm

There are two sections to the algorithm.

First Part

The criterion for the diagonal elements is checked in the first portion. We compare each diagonal element to the following diagonal element to see if they are equivalent. The matrix is not a scalar matrix if the elements are not equal.

Second Part

The condition of non-diagonal items is checked in the second portion. All non-diagonal elements must have a value of zero. The matrix is not a scalar matrix if any non-diagonal entries are not zero.

Example

Input :
Matrix[3][3] = {{3, 0, 0},
             {0, 3, 0},
             {0, 0, 3}} 
Output : Yes


Matrix[4][4] = {{5, 0, 0, 0},
             {0, 3, 0, 0},
             {0, 0, 1, 0},
             {0, 0, 0, 4}} 
Output : No

Program in Java 

The source code for the Java program that checks whether a matrix is a scalar is here.Both sections of the code have been combined into a Scalar_Matrix function, which returns a boolean result after determining whether or not the input matrix is scalar.

Code:

import java.util.*;
Class Scalar_matrix {

static int N = 4;

static boolean Scalar_Matrix(int matrix[][])
{
 //Check whether or not all elements, except the significant diagonal, are zero.               
for (int i = 0; i < N; i++)
	for (int j = 0; j < N; j++)
		if ((i != j) && (matrix[i][j] != 0))
			return false;

//Check to see if all diagonal elements are the same.
for (int i = 0; i < N - 1; i++)
		if (matrix[i][i] != matrix[i + 1][i + 1])
			return false;
return true;
}
public static void main(String args[])
{
int matrix[ ][ ] = { { 1, 0, 0, 0 },
{ 0, 1, 0, 0 },
{ 0, 0, 1, 0 },
{ 0, 0, 0, 1 } };
if (Scalar_Matrix(matrix))
	System.out.println("YES");
else
	System.out.println("NO");
}
}

Output

YES

Program in C++

Both sections of the code have been combined into a Scalar_Matrix function, which returns a boolean result after determining whether or not the input matrix is scalar.

Here is the source code for a C++ application that tests if a matrix is scalar.

Code:

#include <bits/stdc++.h>
#define N 4
using namespace std;
bool Scalar_Matrix(int matrix[N][N])
{
//Check whether or not all elements, except the major diagonal, are zero.    
for (int i = 0; i < N; i++)
	for (int j = 0; j < N; j++)
		if ((i != j) && (matrix[i][j] != 0))
			return false;
//Ensure that none of the Diagonal elements are 0 or not.
for (int i = 0; i < N - 1; i++)
	if (matrix[i][i] != matrix[i + 1][i + 1])
			return false;
return true;
}
int main()
{
int matrix[N][N] = { { 7, 0, 0, 0 },
{ 0, 7, 0, 0 },
{ 0, 0, 7, 0 },
{ 0, 0, 0, 7 } };

if (Scalar_Matrix(matrix))
	cout << "YES" << endl;
else
	cout << "NO" << endl;
return 0;
}

Output

YES

Program in Python

The source code for the python program that checks whether a matrix is a scalar is here.

Both sections of the code have been combined into a Scalar_Matrix function, which returns a boolean result after determining whether or not the input matrix is scalar.

Code:

N = 4
def Scalar_Matrix(mat) :
for i in range(0,N) :
for j in range(0,N) :
if ((i != j) and (matrix[i][j] != 0)) :
	return False

# Check whether all diagonal elements are the same or not.
  for i in range(0,N-1) :
if (matrix[i][i] != matrix[i + 1][i + 1]) :
	return False
return True

matrix = [[ 6, 0, 0, 0 ],
[ 0, 6, 0, 0 ],
[ 0, 0, 6, 0 ],
[ 0, 0, 0, 6 ]]

if (Scalar_Matrix(matrix)):
	print("YES")
else :
	print("NO")

Output

YES

Frequently Asked Questions

What is the method for determining whether a matrix is diagonal?

All entries above and below the main diagonal must be zero for a matrix to be diagonal. The main diagonal can have any amount of zero items.

What is the scalar matrix condition?

A square matrix with the feature that its leading diagonal consists exclusively of a specified scalar while all other entries are 0 is considered a scalar matrix.

Is it true that all diagonal matrices are scalar?

A scalar matrix is a square matrix in which all diagonal components are equal to the same scalar, and all other members are zero.

What exactly is a multi-dimensional array?

An array with more than one dimension is known as a multi-dimensional array. It's an array of arrays or an array with several layers.

Conclusion

In this blog, we have discussed the diagonal and scalar matrix problems. We introduced the scalar and diagonal matrix and then the matrix program in different languages.

We hope this blog has improved your understanding of diagonal and scalar matrix programs.

Check out this problem - Matrix Median

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