Mini Linear Algebra with Openmadness

Linear algebra is a branch of mathematics that helps us work with vectors, matrices, and other multi-dimensional data. Openmadness provides some key operations that let you explore this world without needing a deep math background.

Dot Product

The dot product is a fundamental operation in linear algebra. It's a way to multiply two vectors or matrices and get a single number. You'll often see it in machine learning and data science. In Openmadness, you can use .dot() to calculate it.

Dot product of two vectors

import { omArray } from 'openmadness';

const vectorA = omArray([1, 2, 3]);
const vectorB = omArray([4, 5, 6]);

const dotProduct = vectorA.dot(vectorB);
console.log(dotProduct); // ➝ (1*4 + 2*5 + 3*6) = 4 + 10 + 18 = 32
// Expected output: 32

Matrix multiplication

The dot product is also essential for matrix multiplication. If you have two matrices, you can use .dot() to multiply them.

const matrixA = omArray([
  [1, 2],
  [3, 4]
]);

const matrixB = omArray([
  [5, 6],
  [7, 8]
]);

const productMatrix = matrixA.dot(matrixB);
console.log(productMatrix);
// Expected output:
// [[(1*5 + 2*7), (1*6 + 2*8)],
//  [(3*5 + 4*7), (3*6 + 4*8)]]
// which simplifies to:
// [[19, 22],
//  [43, 50]]

As you can see, Openmadness gives you a simple, chainable way to perform these powerful linear algebra calculations.

Multiply a matrix by a scalar

const M = omArray([
  [1, 2],
  [3, 4]
]);

const result = M.multiply(10);
console.log(result.toArray());
// ➝ [[10, 20], [30, 40]]

This scales every element of the matrix. It is perfect for normalizing or transforming data.