Introduction to Identity Matrix :
The dictionary definition of an Identity Matrix is a square matrix in which all the elements of the principal or main diagonal are 1’s and all other elements are zeros. In the below image, every matrix is an Identity Matrix.
In linear algebra, this is sometimes called as a Unit Matrix, of a square matrix (size = n x n) with ones on the main diagonal and zeros elsewhere. The identity matrix is denoted by “ I “. Sometimes U or E is also used to denote an Identity Matrix.
A property of the identity matrix is that it leaves a matrix unchanged if it is multiplied by an Identity Matrix.
Examples:
Input : 2
Output : 1 0
0 1
Input : 4
Output : 1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
The explanation is simple. We need to make all
the elements of principal or main diagonal as
1 and everything else as 0.
Program to print Identity Matrix :
The logic is simple. You need to the print 1 in those positions where row is equal to column of a matrix and make all other positions as 0.
C/C++
#include<stdio.h>
int Identity(int num)
{
int row, col;
for (row = 0; row < num; row++)
{
for (col = 0; col < num; col++)
{
if (row == col)
printf("%d ", 1);
else
printf("%d ", 0);
}
printf("
");
}
return 0;
}
int main()
{
int size = 5;
identity(size);
return 0;
}
|
Java
class GFG {
static int identity(int num)
{
int row, col;
for (row = 0; row < num; row++)
{
for (col = 0; col < num; col++)
{
if (row == col)
System.out.print( 1+" ");
else
System.out.print( 0+" ");
}
System.out.println();
}
return 0;
}
public static void main(String args[])
{
int size = 5;
identity(size);
}
}
|
Python3
def Identity(size):
for row in range(0, size):
for col in range(0, size):
if (row == col):
print("1 ", end=" ")
else:
print("0 ", end=" ")
print()
size = 5
Identity(size)
|
C#
using System;
class GFG {
static int identity(int num)
{
int row, col;
for (row = 0; row < num; row++)
{
for (col = 0; col < num; col++)
{
if (row == col)
Console.Write( 1+" ");
else
Console.Write( 0+" ");
}
Console.WriteLine();
}
return 0;
}
public static void Main()
{
int size = 5;
identity(size);
}
}
|
PHP
<?php
function Identity($num)
{
$row; $col;
for ($row = 0; $row < $num; $row++)
{
for ($col = 0; $col < $num; $col++)
{
if ($row == $col)
echo 1," ";
else
echo 0," ";
}
echo"
";
}
return 0;
}
$size = 5;
identity($size);
?>
|
Output:
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
Program to check if a given square matrix is Identity Matrix :
C++
#include<iostream>
using namespace std;
const int MAX = 100;
bool isIdentity(int mat[][MAX], int N)
{
for (int row = 0; row < N; row++)
{
for (int col = 0; col < N; col++)
{
if (row == col && mat[row][col] != 1)
return false;
else if (row != col && mat[row][col] != 0)
return false;
}
}
return true;
}
int main()
{
int N = 4;
int mat[][MAX] = {{1, 0, 0, 0},
{0, 1, 0, 0},
{0, 0, 1, 0},
{0, 0, 0, 1}};
if (isIdentity(mat, N))
cout << "Yes ";
else
cout << "No ";
return 0;
}
|
Java
class GFG {
int MAX = 100;
static boolean isIdentity(int mat[][], int N)
{
for (int row = 0; row < N; row++)
{
for (int col = 0; col < N; col++)
{
if (row == col && mat[row][col] != 1)
return false;
else if (row != col && mat[row][col] != 0)
return false;
}
}
return true;
}
public static void main(String args[])
{
int N = 4;
int mat[][] = {{1, 0, 0, 0},
{0, 1, 0, 0},
{0, 0, 1, 0},
{0, 0, 0, 1}};
if (isIdentity(mat, N))
System.out.println("Yes ");
else
System.out.println("No ");
}
}
|
Python3
MAX = 100;
def isIdentity(mat, N):
for row in range(N):
for col in range(N):
if (row == col and
mat[row][col] != 1):
return False;
elif (row != col and
mat[row][col] != 0):
return False;
return True;
N = 4;
mat = [[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]];
if (isIdentity(mat, N)):
print("Yes ");
else:
print("No ");
|
C#
using System;
class GFG {
static bool isIdentity(int[,] mat, int N)
{
for (int row = 0; row < N; row++)
{
for (int col = 0; col < N; col++)
{
if (row == col && mat[row,col] != 1)
return false;
else if (row != col && mat[row,col] != 0)
return false;
}
}
return true;
}
public static void Main()
{
int N = 4;
int [,]mat = {{1, 0, 0, 0},
{0, 1, 0, 0},
{0, 0, 1, 0},
{0, 0, 0, 1}};
if (isIdentity(mat, N))
Console.WriteLine("Yes ");
else
Console.WriteLine("No ");
}
}
|
PHP
<?php
function isIdentity($mat, $N)
{
for ($row = 0; $row < $N; $row++)
{
for ( $col = 0; $col < $N; $col++)
{
if ($row == $col and
$mat[$row][$col] != 1)
return false;
else if ($row != $col &&
$mat[$row][$col] != 0)
return false;
}
}
return true;
}
$N = 4;
$mat = array(array(1, 0, 0, 0),
array(0, 1, 0, 0),
array(0, 0, 1, 0),
array(0, 0, 0, 1));
if (isIdentity($mat, $N))
echo "Yes ";
else
echo "No ";
?>
|
Output:
Yes
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