Organizing Data in Tables

Linear Algebra (Matrices) · Axiom Academy

A matrix has a second face: not a transformation, but a data table — a rectangular grid of numbers you can read by row and column. The other face of a matrix: a data table You may have met a matrix as a machine that transforms space. But a matrix has a quieter, more everyday job too — it organizes data . A spreadsheet of prices across stores, the pixels of an image, a table of distances between cities: each is just numbers laid out in a grid of rows and columns . That grid is a matrix. Here is a price list that arrives as a scattered jumble — every (item, store, price) on its own. Watch it snap into a rectangular grid: items become the rows, stores become the columns, and every price lands in exactly one cell. The instant it has rows and columns, it's a matrix. A pile of numbers becomes a matrix the moment you give it rows and columns — that's all "organizing data in a table" means. Reading a single entry: "row i, column j" Every entry has an address. We write it a_ ij — the number in row i and column j (row first, then column). Drag the two dials to pick a row and a column, and watch the grid point straight at the entry they name. Row first, column second. The row index i and the column index j together pin down exactly one number — no searching. Point at any entry — and size up the whole grid

This is the written version of the interactive lesson above. See the full Linear Algebra (Matrices) course.