The interactive film is in the book's Companion

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Block Diagonal Matrices: Separate Worlds

Chapter 10 · Mathematics for AI and Machine Learning · Beginner · 1:24

An interactive live film: A = blkdiag(A₀, a₁) moves the floor and the heights of a cube separately, so its inverse is blockwise and its volume factor is det A₀ · a₁; an off-diagonal coupling makes the heights leak into the floor.

Narration

The grey cube holds every point with coordinates between zero and one. The matrix A is block diagonal: a two by two block for the floor, and a single number for the height.

The floor block A zero turns the floor square into a slanted parallelogram, and it never sees the heights.

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

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