Program to find Normal and Trace of a matrix

Last Updated : 19 Aug, 2022

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)

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Implementation:

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# 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), since no extra space has been taken.

Data Science | Solving Linear Equations

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Program to find Normal and Trace of a matrix

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