A matrix is a grid of numbers. They encode systems of equations, transformations, and data.
Edit the matrix
A
→
det(A)
10
Non-zero ⇒ A is invertible.
Your turn
How many entries does a 3 × 4 matrix have, and what size is its transpose?
Matrices aren't just for equations. A digital image is a matrix of pixel values; a 3D rotation is a 3×3 matrix; Google's original PageRank was the dominant eigenvector of a giant matrix of links.
Recap
- A matrix is a rectangular grid of numbers, sized m × n (rows × columns).
- Square matrices (n × n) can have a determinant and (sometimes) an inverse.
- The identity I acts like the number 1: AI = IA = A.
Notation
- m × n — m rows, n columns.
- Square — same number of rows and columns.
- Identity I — 1s on diagonal, 0s elsewhere; AI = A.