Linear Algebra

Vectors, matrices, and the transformations of space: the mathematics behind data, graphics, and systems of equations.

What linear algebra is

The study of vectors and the straight-line structure of space, and why it turns up everywhere from graphics to data.

Vectors as both arrows in space and lists of numbers, and the two operations (adding and scaling) that define them.

Matrices as rectangular grids of numbers that also act as machines taking vectors to vectors.

Functions that keep gridlines straight and the origin fixed (rotations, scalings, and shears) and how a matrix encodes one.

The determinant as the factor by which a transformation scales area or volume, and what it says about undoing the transformation.

The special directions a transformation leaves unchanged except for scaling, and why they reveal a matrix's true character.