The interactive film is in the book's Companion

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Diagonalization: Change Basis, Stretch, Change Back

Chapter 6 · Mathematics for AI and Machine Learning · Advanced · 1:44

An interactive live film: four stacked layers show x, V^{-1} x, Lambda V^{-1} x and A x; as the eigenvectors merge the middle layers blow up. Find the c at which A cannot be diagonalized.

Narration

Here is a two by two matrix A acting on colored points of the unit circle. The bottom layer holds the points, the top layer their images A x.

Diagonalization writes A as V lambda V inverse, with the eigenvectors in V. Read it from the right, layer by layer going up.

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

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