Cramer's Rule

A matrix-style method for solving square systems of equations. We bust out a coefficient matrix, track down the determinant D, and swap out each variable column for a constant column to get the new determinants D_x and D_y. To solve for x, divide D_x by D. To solve for y, divide D_y by D. It's got more letters than a Chekhov play, but it's super useful.

Determinant

While it sounds like the name of some cheesy product from an "As Seen On TV" infomercial, it's actually a special number derived from a square matrix. It's useful to know sometimes, and it's written as |A| = ad – bc for a 2 × 2 matrix.

Entries

Each number or variable inside the brackets of a matrix.

Identity Matrix

The matrix version of the number 1, i.e. the best matrix. At least, it thinks that it's #1. More objectively speaking, it's a square matrix with a line of 1s running diagonal from upper-left to lower-right, with the rest of its entries as 0s.

Matrix

Variables or constants arranged like a grid in rows and columns that together make up a rectangle. The rows go across, and the columns are vertical; they're like the columns in the Lincoln Memorial. Here's a 2 × 2 matrix: 

 

Scalar

A constant multiplied throughout a matrix. That doesn't sound exciting, until everything in your matrix is suddenly a thousand times bigger. Hope you packed something good in there!

Square Matrix

A matrix that has the same number of rows and columns. Literally, square matrices look square.

Zero Matrix

The matrix version of the number 0, i.e. a matrix filled with 0s. It can be any size, but try and be reasonable about it.