Skip to content
Related Articles

Related Articles

Improve Article

Program to find Normal and Trace of a matrix

  • Difficulty Level : Basic
  • Last Updated : 13 Apr, 2021

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)

 

 

Untitled

 



C++




// 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



// 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



# 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#



// 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
// 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.
?>
Javascript



<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)
References: 
https://en.wikipedia.org/wiki/Trace_(linear_algebra)
This article is contributed by DANISH_RAZA. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 
Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.



My Personal Notes
arrow_drop_up
Next

Sort a Matrix in all way increasing order
Recommended Articles
Page :
Java Program to Find the Normal and Trace of a Matrix
15, Mar 21
Find trace of matrix formed by adding Row-major and Column-major order of same matrix
04, Dec 17
Maximum trace possible for any sub-matrix of the given matrix
12, Mar 19
Standard Normal Distribution (SND) - Java Program
22, Dec 17
Find normal at a given point on the curve
29, Oct 18
Length of the normal from origin on a straight line whose intercepts are given
16, Apr 19
Game Theory (Normal form game) | Set 2 (Game with Pure Strategy)
31, Jul 19
Game Theory (Normal-form game) | Set 3 (Game with Mixed Strategy)
02, Aug 19
Game Theory (Normal-form Game) | Set 5 (Dominance Property-Mixed Strategy)
10, Dec 19
Game Theory (Normal-form Game) | Set 6 (Graphical Method [2 X N] Game)
18, Dec 19
Game Theory (Normal-form Game) | Set 7 (Graphical Method [M X 2] Game)
18, Dec 19
Multiple Linear Regression Model with Normal Equation
08, Mar 21
Equation of a normal to a Circle from a given point
21, May 21
Game Theory (Normal-form Game) | Set 4 (Dominance Property-Pure Strategy)
10, Dec 19
Generate matrix from given Sparse Matrix using Linked List and reconstruct the Sparse Matrix
19, Apr 21
Generate a Matrix such that given Matrix elements are equal to Bitwise OR of all corresponding row and column elements of generated Matrix
15, Jan 21
Program to check diagonal matrix and scalar matrix
10, Jan 18
Program to check if a matrix is Binary matrix or not
04, Oct 18
Program to convert given Matrix to a Diagonal Matrix
27, Nov 18
C++ program to Convert a Matrix to Sparse Matrix
26, Aug 19
Program to find the Sum of each Row and each Column of a Matrix
31, Oct 18
Check if a given matrix can be converted to another given matrix by row and column exchanges
30, Apr 20
Program to find all types of Matrix
26, Feb 18
Program to find the maximum element in a Matrix
26, Oct 18
Article Contributed By :
https://media.geeksforgeeks.org/auth/avatar.png
GeeksforGeeks
Vote for difficulty
Current difficulty :
Basic





Improved By :
Article Tags :
Practice Tags :
Report Issue

We use cookies to ensure you have the best browsing experience on our website. By using our site, you
acknowledge that you have read and understood our
Cookie Policy &
        Privacy Policy

Lightbox