Linear Algebra and Its Applications · Problem 6.2.24

Positive Definite Matrices — Gilbert Strang

Mathematics · tests-for-positive-definiteness

Problem

For which

s

and

t

A

and

B

have all

\lambda > 0

(and are therefore positive definite)?

A = \begin{bmatrix} s & -4 & -4 \\ -4 & s & -4 \\ -4 & -4 & s \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} t & 3 & 0 \\ 3 & t & 4 \\ 0 & 4 & t \end{bmatrix}.