# Golang Program To Find The Trace And Normal Of A Matrix

In this tutorial, we will write an article to find the normal and trace of a matrix. A matrix is considered normal if its square root equals the sum of the squares of each member and the trace is the total of a matrix's diagonal elements.

## Golang Program To Find The Normal

### Finding Normal of 2x2 Matrix

In this example, we will see how we can find the normal of a 2 X 2 matrix.

### Algorithm

Step 1 − First, we need to import the fmt and math package.

Step 2 − Create a function to find the Normal of the matrix. This function uses two for loops to find the square of each element.

Step 3 − Update the sum variable by adding the square of each element to it. Return the sum variable.

Step 4 − Start the main() function. Initialize a matrix and print it on the screen.

Step 5 − call the findNormal() function by passing the matrix as well as its rank to the function as arguments.

Step 6 − Store the result from the function in a new variable called normal and print it on the screen using fmt.Println() function.

### Example

package main
import (
"fmt"
"math"
)

// function to create normal
func findNormal(mat int, n int) float64 {
var sum int = 0
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
sum += mat[i][j] * mat[i][j]
}
}
var sum1 float64
sum1 = float64(sum)
return math.Sqrt(sum1)
}
func main() {

// initializing a 2 X 2 matrix
mat := int{
{1, 2},
{5, 6},
}
// printing matrix
fmt.Println("The given matrix is: \n")
for i := 0; i < 2; i++ {
for j := 0; j < 2; j++ {
fmt.Print(mat[i][j], "\t")
}
fmt.Println()
}
fmt.Println()
normal := findNormal(mat, 2)
fmt.Println("Normal of Matrix is:", normal)
}


### Output

The given matrix is:

1	2
5	6

Normal of Matrix is: 8.12403840463596


## Find Normal Of A 3 X 3 Matrix

In this example, we will write a go program to find the normal of a 3 X 3 matrix.

### Example

package main
import (
"fmt"
"math"
)

// function to find normal
func findNormal(mat int, n int) float64 {
var sum int = 0
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
sum += mat[i][j] * mat[i][j]
}
}
var sum1 float64
sum1 = float64(sum)
return math.Sqrt(sum1)
}
func main() {

// initializing a 3 X 3 matrix
mat := int{
{0, 1, 2},
{4, 5, 6},
{8, 9, 10},
}

// printing matrix
fmt.Println("The given matrix is: \n")
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
fmt.Print(mat[i][j], "\t")
}
fmt.Println()
}
normal := findNormal(mat, 3)
fmt.Println("\n Normal of Matrix is:", normal)
}


### Output

The given matrix is:

0	1	2
4	5	6
8	9	10

Normal of Matrix is: 18.083141320025124


## Golang Program To Find The Trace

### Finding Trace of 2x2 Matrix

In this example, we will find the trace of a 2 X 2 matrix using user defined function.

### Algorithm

Step 1 − First, we need to import the fmt and math package.

Step 2 − Create a function to find the tace of the matrix. This function uses a for loops to find the sum of diagonal elements.

Step 3 − Update the sum variable by adding each diagonal element to it. Return the sum variable.

Step 4 − Start the main() function. Initialize a matrix and print it on the screen.

Step 5 − call the findNormal() function by passing the matrix as well as its rank as arguments to a function.

Step 6 − Store the result from the function in a new variable called trace and print it on the screen using fmt.Println() function.

### Example

package main
import (
"fmt"
)

// function to create trace
func findTrace(mat int, n int) int {
var sum int = 0
for i := 0; i < n; i++ {
sum += mat[i][i]
}
return sum
}
func main() {

// initializing a 2 X 2 matrix
mat := int{
{10, 20},
{50, 60},
}

// printing matrix
fmt.Println("The given matrix is: \n")
for i := 0; i < 2; i++ {
for j := 0; j < 2; j++ {
fmt.Print(mat[i][j], "\t")
}
fmt.Println()
}
trace := findTrace(mat, 2)
fmt.Println("\nTrace of Matrix is:", trace)
}


### Output

The given matrix is:

10	20
50	60

Trace of Matrix is: 70


### Find Trace Of A 3 X 3 Matrix

In this example, we will write a go program code to find the trace of 3 X 3 matrix.

### Example

package main
import (
"fmt"
)

// function to create trace
func findTrace(mat int, n int) int {
var sum int = 0
for i := 0; i < n; i++ {
sum += mat[i][i]
}
return sum
}
func main() {

// initializing a 3 X 3 matrix
mat := int{
{5, 7, 9},
{2, 4, 6},
{1, 3, 8},
}

// printing matrix
fmt.Println("The given matrix is: \n")
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
fmt.Print(mat[i][j], "\t")
}
fmt.Println()
}
trace := findTrace(mat, 3)
fmt.Println("\nTrace of Matrix is:", trace)
}


### Output

The given matrix is:

5	7	9
2	4	6
1	3	8

Trace of Matrix is: 17


## Conclusion

Successfully compiled and executed a golang program to find the normal and trace of matrices along with examples.

Updated on: 02-Jan-2023

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