Linear Algebra (Go)

Utilities for working with matrices and vectors in Go. This module provides core linear algebra routines (row-reduced echelon form, dot products, identity matrices, scalar operations, basic validation helpers) and a small demo app under cmd/graph that renders simple 2D vectors to an image.

Project structure

• go.mod — Go module github.com/igomez10/linearalgebra
• main.go — Library package linearalgebra with matrix/vector helpers
• main_test.go — Unit tests for the library
• cmd/graph/ — Demo app that draws vectors and saves 3dplot.png
  • main.go — Render a simple grid and a few vectors
  • main_test.go — Tests for rendering helpers
• python/main_unitest.py — A small Python unittest example (unrelated to the Go module; useful for teaching/tests)

Requirements

• Go 1.23+

Install

Add the module to your project:

go get github.com/igomez10/linearalgebra@latest

Then import it in your code:

import "github.com/igomez10/linearalgebra"

Quick start (library)

1) Row-Reduced Echelon Form (RREF)

package main

import (
    "fmt"
    la "github.com/igomez10/linearalgebra"
)

func main() {
    A := [][]float64{{1, 2, 3}, {2, 5, 3}, {1, 0, 8}}
    rref := la.ToRowReducedEchelonForm(A)
    fmt.Println("RREF:", rref)
}

2) Matrix multiplication (dot product)

A := [][]float64{{1, 2}, {3, 4}} // 2x2
B := [][]float64{{5, 6}, {7, 8}} // 2x2
C := linearalgebra.DotProduct(A, B)
// C = [[19, 22], [43, 50]]

3) Identity matrix and scalar ops

I := linearalgebra.GenerateIdentityMatrix(3) // 3x3 identity
J := linearalgebra.MultiplyMatrixByScalar(I, 2) // every entry *2

4) Vector dot product

u := []float64{1, 2, 3}
v := []float64{4, 5, 6}
dp := linearalgebra.DotProductVectors(u, v) // 1*4 + 2*5 + 3*6 = 32

Common helpers you’ll find in the package include:

• ToRowReducedEchelonForm(matrix [][]float64) [][]float64
• DotProduct(A, B [][]float64) [][]float64
• DotProductVectors(a, b []float64) float64
• GenerateIdentityMatrix(n int) [][]float64
• AddMatrices(A, B [][]float64) [][]float64
• MultiplyMatrixByScalar(M [][]float64, s float64) [][]float64
• MultiplyRowByScalar(M [][]float64, row int, s float64) [][]float64
• AddRowToRow(M [][]float64, row []float64, idx int) [][]float64
• CanMultiplyMatrices(A, B [][]float64) bool
• IsZeroMatrix(M [][]float64) bool

Note: Some functions may panic on illegal operations (e.g., dimension mismatch); validate inputs with helpers like CanMultiplyMatrices first.

Demo app: draw vectors to an image

There’s a small program under cmd/graph that renders a grid and a few 2D vectors, saving the result as 3dplot.png.

Run it:

go run ./cmd/graph

You should see a 3dplot.png file created in cmd/graph/ with axis lines and example vectors.

Testing

Run all Go tests:

go test ./...

The demo also has its own tests:

go test ./cmd/graph

Optional Python example (requires NumPy):

python3 python/main_unitest.py

Notes and roadmap

• The library focuses on clarity and teaching; some routines are not optimized for large matrices.
• Future ideas: determinants, inverses, LU/QR decompositions, eigenvalues/eigenvectors, and improved numerical stability.