# Find trace and normal of matrix in C++

This C++ program is able to find the **trace and normal of a matrix** in the same way that we find in mathematics.

Basically the

traceof a matrix is the sum of main diagonal of a matrix andnormalis square root of sum of all the elements.

Similar to all other operations applicable on a matrix, this program is also possible to perform in a much simple and time efficient manner by the use of programming. Instead of manually doing these jobs, writing some lines of code which will work for us is better. I am going to show you how.

## Trace and normal of a matrix in C++

**Methodology**

- Define a matrix(integer array) and assign values for the matrix.
- Define separate variables to store normal, trace and dimensions of array.
- To find normal the sum of all the elements and then the square root of the result and store it in a variable.
- To find trace find the sum of main diagonal elements where row and column dimensions are equal for matrix the store the result in a variable.
- Print the result on screen.

**Program**

Following is the program code to **find trace and normal of a matrix**. It is written and successfully compiled in CodeBlocks v 16.01 in windows 10.

#include <iostream> #include<math.h> using namespace std; int main() { int matrix[3][3]={{2,3,5},{7,4,5},{8,5,4}}; //declaration and values assignment of array int trace=0; float normal; for(int i=0;i<3;i++){ for(int j=0;j<3;j++){ normal=normal+matrix[i][j]; //sum of all elements if(i==j) // condition for trace of matrix trace=trace+matrix[i][j]; } } normal=sqrt(normal); //sqrt() id defined in math.h header file cout<<"Following is the matrix"<<endl; for(int i=0;i<3;i++){ // print matrix elements for(int j=0;j<3;j++) cout<<matrix[i][j]<<"\t"; cout<<endl; } cout<<"Normal of matrix: "<<normal<<endl; cout<<"Trace of matrix: "<<trace<<endl; }

**Output**

Following is the matrix 2 3 5 7 4 5 8 5 4 Normal of matrix: 6.55744 Trace of matrix: 10

**Program ****explanation**

- Declare a matrix of size 3X3 assigned values to it.
- Declare variables, normal as float and trace as int.
- Run a nested for loop to sum all the elements values in normal variable.
- Along with this use if condition as row==column then sum diagonal elements in trace variable.
- Perform the square root of the normal variable by using predefined function sqrt().
- Print the matrix elements followed by trace and normal variables on the screen.

Also, read

Find the next greater number from the same set of digits in C++

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