Program to find Normal and Trace of a matrix
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)
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. ?> |
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)
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