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### Episode 23a (28:01): Totally, for sure, Positive Definite Matrices

#### Summary:

We venture into a world of elegant square matrices, the ones of Positive Definiteness. For our purposes, Positive Definite Matrices (PDMs) are real, symmetric, square matrices that have only positive eigenvalues ($\lambda_i > 0 \ \forall\ i$). We develop a test for PDMness and find a surprising connection between pivots and eigenvalues: their signs must match up. Theory first in this episode, and then example usages in the ones following.