Linear Algebra and Its Applications · Problem 6.1.8

Positive Definite Matrices — Gilbert Strang

Mathematics · positive-definite-matrices-minima-maxima-saddle-points

Problem

A = \begin{bmatrix} a & b \\ b & c \end{bmatrix}

is positive definite, test

A^{-1} = \begin{bmatrix} p & q \\ q & r \end{bmatrix}

for positive definiteness.