matrix

A matrix is a tidy grid of numbers, like a spreadsheet or a seating chart: numbers lined up in rows that run left to right and columns that run top to bottom. Instead of writing many separate numbers scattered around, you pack them into one rectangular block so you can work with the whole bundle at once.

Formally, a matrix is a rectangular array of numbers (or other objects) arranged in m rows and n columns; we call it an m-by-n matrix. The plural is matrices. A single matrix usually gets a capital letter like A, and people often draw big brackets around the grid. The numbers inside are called the entries.

Matrices are not just decoration: they are a compact language for storing data and for describing transformations like rotations, scalings, and the coefficients of a system of equations. Much of linear algebra is the study of what you can do with these grids — adding them, multiplying them, inverting them — and what those operations mean.