Matrices

A spreadsheet of sales — rows for products, columns for months — is a matrix: a rectangular grid of numbers. What's surprising is that such grids have their own algebra. You can add them, scale them, and even multiply two grids together in a way that composes their effects. Matrices solve systems of equations in bulk, rotate images in graphics, and rank web pages at Google. The grid isn't just a storage format; it's a mathematical object with superpowers.