The interactive film is in the book's Companion

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A Matrix Moves the Cube

Chapter 2 · Mathematics for AI and Machine Learning · Advanced · 1:53

An interactive live film: the columns of a 3 x 3 matrix are where the edges of the unit cube go; A x is a walk along them (column view) and its entries are rows dotted with x (row view). Drag a column tip and its numbers change, drag a number and the box follows; flatten the box to rank two.

Narration

Here is the unit cube, in grey, and a three by three matrix A. Each column of A tells where one edge of the cube goes.

The first column, a zero, in red, is where the first edge lands. The second, a one, in blue, and the third, a two, in green, are the other two. Together they span a slanted box: the image of the cube.

The rest of the narration is in the book's Companion.

More from Chapter 2

Interactive1:40Change of Basis: One Vector, Two Sets of CoordinatesChapter 2Preview1:29The Matrix Inverse: Squashed Means GoneChapter 2Preview1:49Rank One as a LandscapeChapter 2Preview2:29Four Views of Matrix MultiplicationChapter 2Preview1:44Column Space: Every Output Ax Lies on One PlaneChapter 2Preview1:37The Projection Matrix: Outer times Inverse InnerChapter 2Preview1:36Matrix Norm and Condition Number: the Largest StretchChapter 2