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The Derivative of the Matrix Inverse

Chapter 11 · Mathematics for AI and Machine Learning · Advanced · 1:43

An interactive live film: 2 x 2 symmetric matrices as points in 3D, the cone of positive definite ones, and the Frechet derivative of the inverse as a straight-line prediction whose error falls like epsilon squared.

Narration

Every two by two symmetric matrix is a point in space: its two diagonal entries along the floor, and its off diagonal entry going up. The positive definite matrices fill this cone.

Here is a matrix X inside the cone, and its inverse, another point in the same cone.

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

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