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⇱ Program to find Normal and Trace of a matrix - GeeksforGeeks


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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)

👁 Untitled

Implementation:


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.

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