Linear Algebra and Its Applications · Problem 6.1.18

Positive Definite Matrices — Gilbert Strang

Mathematics · positive-definite-matrices-tests-for-positive-definiteness

Problem

Test to see if

A^T A

is positive definite in each case:

A = \begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix}, \quad A = \begin{bmatrix} 1 & 1 \\ 1 & 2 \\ 2 & 1 \end{bmatrix}, \quad \text{and} \quad A = \begin{bmatrix} 1 & 1 & 2 \\ 1 & 2 & 1 \end{bmatrix}.