Program to find Normal and Trace of a matrix
Last Updated :
19 Aug, 2022
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Given a 2D matrix, the task is to find Trace and Normal of matrix.
Normal of a matrix is defined as square root of sum of squares of matrix elements.
Trace of a n x n square matrix is sum of diagonal elements.
Examples :
Input : mat[][] = {{7, 8, 9},
{6, 1, 2},
{5, 4, 3}};
Output : Normal = 16
Trace = 11
Explanation :
Normal = sqrt(7*7+ 8*8 + 9*9 + 6*6 +
1*1 + 2*2 + 5*5 + 4*4 + 3*3)
= 16
Trace = 7+1+3 = 11
Input :mat[][] = {{1, 2, 3},
{6, 4, 5},
{2, 1, 3}};
Output : Normal = 10
Trace = 8
Explanation :
Normal = sqrt(1*1 +2*2 + 3*3 + 6*6 + 4*4 +
5*5 + 2*2 + 1*1 + 3*3)
Trace = 8(1+4+3)
Implementation:
// C++ program to find trace and normal
// of given matrix
#include<bits/stdc++.h>
using namespace std;
// Size of given matrix
const int MAX = 100;
// Returns Normal of a matrix of size n x n
int findNormal(int mat[][MAX], int n)
{
int sum = 0;
for (int i=0; i<n; i++)
for (int j=0; j<n; j++)
sum += mat[i][j]*mat[i][j];
return sqrt(sum);
}
// Returns trace of a matrix of size n x n
int findTrace(int mat[][MAX], int n)
{
int sum = 0;
for (int i=0; i<n; i++)
sum += mat[i][i];
return sum;
}
// Driven source
int main()
{
int mat[][MAX] = {{1, 1, 1, 1, 1},
{2, 2, 2, 2, 2},
{3, 3, 3, 3, 3},
{4, 4, 4, 4, 4},
{5, 5, 5, 5, 5},
};
cout << "Trace of Matrix = "
<< findTrace(mat, 5) << endl;
cout << "Normal of Matrix = "
<< findNormal(mat, 5) << endl;
return 0;
}
// Java program to find trace and normal
// of given matrix
import java.io.*;
class GFG {
// Size of given matrix
static int MAX = 100;
// Returns Normal of a matrix of size n x n
static int findNormal(int mat[][], int n)
{
int sum = 0;
for (int i=0; i<n; i++)
for (int j=0; j<n; j++)
sum += mat[i][j]*mat[i][j];
return (int)Math.sqrt(sum);
}
// Returns trace of a matrix of size n x n
static int findTrace(int mat[][], int n)
{
int sum = 0;
for (int i=0; i<n; i++)
sum += mat[i][i];
return sum;
}
// Driven source
public static void main (String[] args) {
int mat[][] = {{1, 1, 1, 1, 1},
{2, 2, 2, 2, 2},
{3, 3, 3, 3, 3},
{4, 4, 4, 4, 4},
{5, 5, 5, 5, 5},
};
System.out.println ("Trace of Matrix = "
+ findTrace(mat, 5));
System.out.println ("Normal of Matrix = "
+ findNormal(mat, 5));
}
}
// This code is contributed by vt_m.
# Python3 program to find trace and
# normal of given matrix
import math
# Size of given matrix
MAX = 100;
# Returns Normal of a matrix
# of size n x n
def findNormal(mat, n):
sum = 0;
for i in range(n):
for j in range(n):
sum += mat[i][j] * mat[i][j];
return math.floor(math.sqrt(sum));
# Returns trace of a matrix of
# size n x n
def findTrace(mat, n):
sum = 0;
for i in range(n):
sum += mat[i][i];
return sum;
# Driver Code
mat = [[1, 1, 1, 1, 1],
[2, 2, 2, 2, 2],
[3, 3, 3, 3, 3],
[4, 4, 4, 4, 4],
[5, 5, 5, 5, 5]];
print("Trace of Matrix =", findTrace(mat, 5));
print("Normal of Matrix =", findNormal(mat, 5));
# This code is contributed by mits
// C# program to find trace and normal
// of given matrix
using System;
class GFG {
// Returns Normal of a matrix of
// size n x n
static int findNormal(int [,]mat, int n)
{
int sum = 0;
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
sum += mat[i,j] * mat[i,j];
return (int)Math.Sqrt(sum);
}
// Returns trace of a matrix of size
// n x n
static int findTrace(int [,]mat, int n)
{
int sum = 0;
for (int i = 0; i < n; i++)
sum += mat[i,i];
return sum;
}
// Driven source
public static void Main ()
{
int [,]mat = { {1, 1, 1, 1, 1},
{2, 2, 2, 2, 2},
{3, 3, 3, 3, 3},
{4, 4, 4, 4, 4},
{5, 5, 5, 5, 5},
};
Console.Write ("Trace of Matrix = "
+ findTrace(mat, 5) + "\n");
Console.Write("Normal of Matrix = "
+ findNormal(mat, 5));
}
}
// This code is contributed by nitin mittal.
<?php
// PHP program to find trace and
// normal of given matrix
// Size of given matrix
$MAX = 100;
// Returns Normal of a
// matrix of size n x n
function findNormal($mat, $n)
{
$sum = 0;
for ( $i = 0; $i < $n; $i++)
for ( $j = 0; $j < $n; $j++)
$sum += $mat[$i][$j] *
$mat[$i][$j];
return floor(sqrt($sum));
}
// Returns trace of a
// matrix of size n x n
function findTrace( $mat, $n)
{
$sum = 0;
for ( $i = 0; $i < $n; $i++)
$sum += $mat[$i][$i];
return $sum;
}
// Driver Code
$mat = array(array(1, 1, 1, 1, 1),
array(2, 2, 2, 2, 2),
array(3, 3, 3, 3, 3),
array(4, 4, 4, 4, 4),
array(5, 5, 5, 5, 5));
echo "Trace of Matrix = ",
findTrace($mat, 5),"\n";
echo "Normal of Matrix = " ,
findNormal($mat, 5) ;
// This code is contributed by anuj_67.
?>
<script>
// Javascript program to find trace
// and normal of given matrix
// Size of given matrix
var MAX = 100;
// Returns Normal of a matrix of size n x n
function findNormal(mat, n)
{
var sum = 0;
for(var i = 0; i < n; i++)
for(var j = 0; j < n; j++)
sum += mat[i][j] * mat[i][j];
return parseInt(Math.sqrt(sum));
}
// Returns trace of a matrix of size n x n
function findTrace(mat, n)
{
var sum = 0;
for(var i = 0; i < n; i++)
sum += mat[i][i];
return sum;
}
// Driver code
var mat = [ [ 1, 1, 1, 1, 1 ],
[ 2, 2, 2, 2, 2 ],
[ 3, 3, 3, 3, 3 ],
[ 4, 4, 4, 4, 4 ],
[ 5, 5, 5, 5, 5 ] ];
document.write("Trace of Matrix = " +
findTrace(mat, 5) + "<br>");
document.write("Normal of Matrix = " +
findNormal(mat, 5));
// This code is contributed by Kirti
</script>
Output
Trace of Matrix = 15 Normal of Matrix = 16
Time Complexity : O(n*n)
Space Complexity : O(1), since no extra space has been taken.
