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:
// 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;
} |
// 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 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. |
// 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 // 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 ?> |
<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> |
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:
// 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;
} |
// 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. |
# 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. |
// 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 // 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 ?> |
<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> |
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.