The interactive film is in the book's Companion

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Cholesky: a Square Root That Exists Only for Positive Definite Matrices

Chapter 7 · Mathematics for AI and Machine Learning · Advanced · 1:35

An interactive live film: the book's Cholesky algorithm runs live on a matrix with one free entry b; the ellipsoid x^T A x = 1 stretches until the last square root fails. Find the largest b for which Cholesky works.

Narration

Here is the matrix from the book's example, except that one pair of entries is now a number b. With b equal to one, it is the example.

Cholesky builds a lower triangular L, row by row, with A equal to L L transposed. Each row first solves a small triangular system, then takes a square root for its diagonal entry.

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

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