**How to find trace of a matrix: **In the previous article, we have discussed Python Program to Print Odd Numbers in Given Range Using Recursion

Given a matrix and the task is to find the normal and trace of the given Matrix in Python.

**What is a matrix:**

**Trace of a matrix python: **A matrix is a rectangular sequence of numbers divided into columns and rows. A matrix element or entry is a number that appears in a matrix.

**Example:**

Above is the matrix which contains 5 rows and 4 columns and having elements from 1 to 20.

In this order, the dimensions of a matrix indicate the number of rows and columns.

Here as there are 5 rows and 4 columns it is called a 5*4 matrix.

- Python Program for Sum of Middle Row and Column in Matrix
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**Normal of a matrix:**

The sum of squares is normal for all the matrix entries.

**Trace of a matrix:**

Trace is the sum of the Matrix’s diagonal parts.

**Examples:**

**Example1:**

**Input:**

Given Matix : 2 6 4 8 5 3 1 6 8

**Output:**

The trace value of the given matrix is : 15 The normal value of the given matrix is : 6.557438524302

**Example2:**

**Input:**

Given Matix : 1 2 3 4 7 5 8 6 9 4 2 5 1 1 1 1

**Output:**

The trace value of the given matrix is : 9 The normal value of the given matrix is : 7.745966692414834

## Program to find the Normal and Trace of a Matrix in Python

Below are the ways to find the normal and trace of the given Matrix in Python:

### Method #1: Using For Loop (Static Input)

**Approach:**

- Import the math module using the import keyword.
- Give the matrix as static input and store it in a variable.
- Calculate the number of rows of the given matrix by calculating the length of the nested list using the len() function and store it in a variable
**mtrxrows**. - Calculate the number of columns of the given matrix by calculating the length of the first list in the nested list using the len() function and store it in a variable
**mtrxcolums**. - Take a variable say
**mtrxtrace**which stores the trace of the given matrix and initialize its value to 0. - Take a variable say
**mtrxsum**which stores the sum of all elements of the matrix and initialize its value to 0. - Loop till the given number of rows using the For loop.
- Inside the For loop, Iterate till the given number of columns using another Nested For loop(Inner For loop).
- Check if the parent loop iterator value is equal to the inner loop iterator value using the if conditional statement(This is whether the element is diagonal element or not)
- If it is true then add this value to
**mtrxtrace.** - After the if conditional statement, Add the gvnmatrix[n][m] to the above-initialized
**mtrxsum**and store it in the same variable**mtrxsum.** - After the end of two loops calculate the square root of the
**mtrxsum**value using the sqrt() function and store this result in**mtrxnormal**variable. - Print the value of
**mtrxtrace**which gives the value of the trace of the given matrix. - Print the value of
**mtrxnormal**which gives the value of the normal of the given matrix. - The Exit of the Program.

**Below is the implementation:**

# Import the math module using the import keyword. import math # Give the matrix as static input and store it in a variable. mtrx = [[2, 6, 4], [8, 5, 3], [1, 6, 8]] # Calculate the number of rows of the given matrix by # calculating the length of the nested list using the len() function # and store it in a variable mtrxrows. mtrxrows = len(mtrx) # Calculate the number of columns of the given matrix by # calculating the length of the first list in the nested list # using the len() function and store it in a variable mtrxcols. mtrxcols = len(mtrx[0]) # Take a variable say mtrxtrace which stores the trace of the given matrix # and initialize its value to 0. mtrxtrace = 0 # Take a variable say mtrxsum which stores the sum of all elements of the matrix # and initialize its value to 0. mtrxsum = 0 # Loop till the given number of rows using the For loop. for n in range(mtrxrows): # Inside the For loop, Iterate till the given number of columns using another # Nested For loop(Inner For loop). for m in range(mtrxcols): # Check if the parent loop iterator value is equal to the inner loop iterator value # using the if conditional statement # (This is whether the element is diagonal element or not) if(n == m): # If it is true then add this value to mtrxtrace. mtrxtrace = mtrxtrace+mtrx[n][m] # After the if conditional statement, # Add the gvnmatrix[n][m] to the above-initialized mtrxsum # and store it in the same variable mtrxsum. mtrxsum = mtrxsum+mtrx[n][m] # After the end of two loops calculate the square root of the mtrxsum value # using the sqrt() function # and store this result in mtrxnormal variable. mtrxnormal = math.sqrt(mtrxsum) # Print the value of mtrxtrace which gives the value of the trace of the given matrix. print('The trace value of the given matrix is :', mtrxtrace) # Print the value of mtrxnormal which gives the value of the normal of the given matrix. print('The normal value of the given matrix is :', mtrxnormal)

**Output:**

The trace value of the given matrix is : 15 The normal value of the given matrix is : 6.557438524302

### Method #2: Using For loop (User Input)

**Approach:**

- Import the math module using the import keyword.
- Give the number of rows of the matrix as user input using the int(input()) function and store it in a variable.
- Give the number of columns of the matrix as user input using the int(input()) function and store it in another variable.
- Take a list and initialize it with an empty value using [] or list() to say
**gvnmatrix**. - Loop till the given number of rows using the For loop
- Inside the For loop, Give all the row elements of the given Matrix as a list using the list(),map(),int(),split() functions and store it in a variable.
- Add the above row elements list to
**gvnmatrix**using the append() function. - Take a variable say
**mtrxtrace**which stores the trace of the given matrix and initialize its value to 0. - Take a variable say
**mtrxsum**which stores the sum of all elements of the matrix and initialize its value to 0. - Loop till the given number of rows using the For loop.
- Inside the For loop, Iterate till the given number of columns using another Nested For loop(Inner For loop).
- Check if the parent loop iterator value is equal to the inner loop iterator value using the if conditional statement(This is whether the element is diagonal element or not)
- If it is true then add this value to
**mtrxtrace.** - After the if conditional statement, Add the gvnmatrix[n][m] to the above-initialized
**mtrxsum**and store it in the same variable**mtrxsum.** - After the end of two loops calculate the square root of the
**mtrxsum**value using the sqrt() function and store this result in**mtrxnormal**variable. - Print the value of
**mtrxtrace**which gives the value of the trace of the given matrix. - Print the value of
**mtrxnormal**which gives the value of the normal of the given matrix. - The Exit of the Program.

**Below is the implementation:**

# Import the math module using the import keyword. import math # Give the number of rows of the matrix as user input using the int(input()) function # and store it in a variable. mtrxrows = int(input('Enter some random number of rows of the matrix = ')) # Give the number of columns of the matrix as user input using the int(input()) function # and store it in another variable. mtrxcols = int(input('Enter some random number of columns of the matrix = ')) # Take a list and initialize it with an empty value using [] or list() to say gvnmatrix. mtrx = [] # Loop till the given number of rows using the For loop for n in range(mtrxrows): # Inside the For loop, Give all the row elements of the given Matrix as a list using # the list(),map(),int(),split() functions and store it in a variable. l = list(map(int, input( 'Enter {'+str(mtrxcols)+'} elements of row {'+str(n+1)+'} separated by spaces = ').split())) # Add the above row elements list to gvnmatrix using the append() function. mtrx.append(l) # Take a variable say mtrxtrace which stores the trace of the given matrix # and initialize its value to 0. mtrxtrace = 0 # Take a variable say mtrxsum which stores the sum of all elements of the matrix # and initialize its value to 0. mtrxsum = 0 # Loop till the given number of rows using the For loop. for n in range(mtrxrows): # Inside the For loop, Iterate till the given number of columns using another # Nested For loop(Inner For loop). for m in range(mtrxcols): # Check if the parent loop iterator value is equal to the inner loop iterator value # using the if conditional statement # (This is whether the element is diagonal element or not) if(n == m): # If it is true then add this value to mtrxtrace. mtrxtrace = mtrxtrace+mtrx[n][m] # After the if conditional statement, # Add the gvnmatrix[n][m] to the above-initialized mtrxsum # and store it in the same variable mtrxsum. mtrxsum = mtrxsum+mtrx[n][m] # After the end of two loops calculate the square root of the mtrxsum value # using the sqrt() function # and store this result in mtrxnormal variable. mtrxnormal = math.sqrt(mtrxsum) # Print the value of mtrxtrace which gives the value of the trace of the given matrix. print('The trace value of the given matrix is :', mtrxtrace) # Print the value of mtrxnormal which gives the value of the normal of the given matrix. print('The normal value of the given matrix is :', mtrxnormal)

**Output:**

Enter some random number of rows of the matrix = 4 Enter some random number of columns of the matrix = 4 Enter {4} elements of row {1} separated by spaces = 1 2 3 4 Enter {4} elements of row {2} separated by spaces = 7 5 8 6 Enter {4} elements of row {3} separated by spaces = 9 4 2 5 Enter {4} elements of row {4} separated by spaces = 1 1 1 1 The trace value of the given matrix is : 9 The normal value of the given matrix is : 7.745966692414834

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