How to implement basic linear algebra operations (vector addition, dot product) in Go?

To implement basic linear algebra operations in Go, you can define custom types and methods for vectors and matrices. Here's an example implementation of vector addition and dot product operations:

package main

import (
	"fmt"
)

// Vector represents a vector in n-dimensional space
type Vector []float64

// Add adds two vectors element-wise
func (v Vector) Add(w Vector) Vector {
	if len(v) != len(w) {
		panic("Vector dimensions mismatch!")
	}

	result := make(Vector, len(v))
	for i := range v {
		result[i] = v[i] + w[i]
	}
	return result
}

// Dot calculates the dot product of two vectors
func (v Vector) Dot(w Vector) float64 {
	if len(v) != len(w) {
		panic("Vector dimensions mismatch!")
	}

	result := 0.0
	for i := range v {
		result += v[i] * w[i]
	}
	return result
}

func main() {
	v := Vector{1, 2, 3}
	w := Vector{4, 5, 6}

	fmt.Println("Vector Addition:", v.Add(w))
	fmt.Println("Dot Product:", v.Dot(w))
}

This code defines a Vector type as a simple slice of float64 values. The Add method adds two vectors element-wise, and the Dot method calculates the dot product of two vectors.

In the main function, an example usage is demonstrated by creating two vectors v and w, and then calling the Add and Dot methods on them.

When working with higher-dimensional vectors or matrices, you may need additional operations like scalar multiplication, matrix addition, matrix multiplication, etc. You can define similar methods for those operations following a similar approach.