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Schur Complement: What Is Left After Minimizing Out a Block

Chapter 10 · Mathematics for AI and Machine Learning · Advanced · 1:40

An interactive live film: the quadratic form of a two-block matrix as a 3D bowl; minimizing over x0 slice by slice traces a valley of height S x1^2, and strengthening the coupling shrinks S to zero and turns the bowl into a saddle.

Narration

Here is a symmetric matrix with two blocks, drawn as its quadratic form, x transpose A x, a bowl over the plane of x zero and x one.

Fix x one, and look along x zero. The slice is a parabola, and its lowest point is the best x zero for that x one.

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

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