Linear Algebra and Its Applications · Problem 6.2.32

Positive Definite Matrices — Gilbert Strang

Mathematics · tests-for-positive-definiteness

Problem

Apply any three tests to each of the matrices

A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 0 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} 2 & 1 & 2 \\ 1 & 1 & 1 \\ 2 & 1 & 2 \end{bmatrix},

to decide whether they are positive definite, positive semidefinite, or indefinite.