# Golang : Linear algebra and matrix calculation example

Continuing from our previous tutorial on how to create matrix with Gonum, we will explore how to perform matrix and linear algebra calculations in this tutorial. Honestly, I found that `NumPy` is more elegant in handling matrix in Python, but since we are in Golang, we will stick to what is available.

Here you go!

`````` package main

import (
"fmt"
"github.com/gonum/matrix/mat64"
)

func main() {
// first there was a void and then
// this matrix is created...
// ⎡1  2  3⎤
// ⎢4  5  6⎥
// ⎣7  8  9⎦

row1 := []float64{1, 2, 3}
row2 := []float64{4, 5, 6}
row3 := []float64{7, 8, 9}

m := mat64.NewDense(3, 3, nil)
m.SetRow(0, row1)
m.SetRow(1, row2)
m.SetRow(2, row3)

// print all m elements
fmt.Printf("m :\n%v\n\n", mat64.Formatted(m, mat64.Prefix(""), mat64.Excerpt(0)))

// then followed by the matrix transpose
mT := m.T()

// print all mT elements
fmt.Printf("mT :\n%v\n\n", mat64.Formatted(mT, mat64.Prefix(""), mat64.Excerpt(0)))

// the matrices decided to go forth and multiply...
//mX := m * mT

mX := mat64.NewDense(3, 3, nil) // a new nil matrix of 3 x 3
mX.MulElem(m, mT)

// print all mX elements
fmt.Printf("mX :\n%v\n\n", mat64.Formatted(mX, mat64.Prefix(""), mat64.Excerpt(0)))

// and add another matrix to make another family member...
mA := mat64.NewDense(3, 3, nil)

// print all mA elements
fmt.Printf("mA :\n%v\n", mat64.Formatted(mA, mat64.Prefix(""), mat64.Excerpt(0)))
fmt.Println(" = ")
fmt.Printf("mX :\n%v\n", mat64.Formatted(mX, mat64.Prefix(""), mat64.Excerpt(0)))
fmt.Println(" + ")
fmt.Printf("mT :\n%v\n\n", mat64.Formatted(mT, mat64.Prefix(""), mat64.Excerpt(0)))

// in order to be more fruitful, first...one must find the determination (determinant)

determinant := mat64.Det(mX)
fmt.Println("Determinant of mX : ", determinant)

// with strong determination (determinant), then linear algebra operations can be solved ....

err := mX.Solve(mX, m)
fmt.Println("Any error? : ", err)

fmt.Printf("Solved mX :\n%v\n", mat64.Formatted(mX, mat64.Prefix(""), mat64.Excerpt(0)))
}
``````

Output:

m :

⎡1 2 3⎤

⎢4 5 6⎥

⎣7 8 9⎦

mT :

⎡1 4 7⎤

⎢2 5 8⎥

⎣3 6 9⎦

mX :

⎡ 1 8 21⎤

⎢ 8 25 48⎥

⎣21 48 81⎦

mA :

⎡ 2 12 28⎤

⎢10 30 56⎥

⎣24 54 90⎦

=

mX :

⎡ 1 8 21⎤

⎢ 8 25 48⎥

⎣21 48 81⎦

+

mT :

⎡1 4 7⎤

⎢2 5 8⎥

⎣3 6 9⎦

Determinant of mX : -360.00000000000006

Any error? :

Solved mX :

⎡ -0.48333333333333306 -0.31666666666666626 -0.1499999999999994⎤

⎢ 0.6666666666666663 0.33333333333333287 -6.614094614788165e-16⎥

⎣ -0.18333333333333318 -0.01666666666666651 0.15000000000000024⎦

References:

https://socketloop.com/tutorials/golang-create-matrix-with-gonum-matrix-package-example

https://godoc.org/github.com/gonum/matrix/mat64#Dense.MulElem

#### See also : Golang : Create matrix with Gonum Matrix package example

##### By Adam Ng

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