---
title: "Algebra Utilities in JavaScript with @kanaries/ml"
description: "Use lightweight linear algebra helpers from the @kanaries/ml Algebra JavaScript and TypeScript implementation in browser and Node.js applications."
canonical_url: "https://ml.kanaries.net/docs/apis/algebra"
markdown_url: "https://ml.kanaries.net/docs/apis/algebra/index.html.md"
---
# Algebra Utilities in JavaScript

## Algorithm overview

The Algebra module contains small matrix helpers used by the library and useful in application-level numeric code: transposition, Gaussian elimination, identity matrices, matrix augmentation, determinants, cofactors, and elementary matrix inverse.

## JavaScript implementation

`@kanaries/ml` exports these helpers under `Algebra`, so simple linear algebra operations can run in browser or Node.js without another dependency.

## Quick start example

```ts
import { Algebra } from '@kanaries/ml';

const X = [[1, 2], [3, 4]];
const XT = Algebra.transpose(X);
const determinant = Algebra.det(X);
const inverse = Algebra.Inverse.elementary(X);
```

## Detailed API reference

```ts
Algebra.transpose(matrix: number[][]): number[][]
Algebra.identityMatrix(A: number[][]): number[][]
Algebra.augmentMatrix(matrix: number[][], expanded: number[][]): number[][]
Algebra.gaussianElimination(A: number[][]): number[][] | false
Algebra.cofactorMatrix(matrix: number[][], minorRowIndex: number, minorColIndex: number): number[][]
Algebra.det(matrix: number[][]): number
Algebra.Inverse.elementary(A: number[][]): number[][] | false
```

`det` requires a non-empty square matrix. Inverse and elimination helpers return `false` when the matrix cannot be reduced with the available pivot logic.