Linear Algebra and Its Applications · Problem 6.2.1

Positive Definite Matrices — Gilbert Strang

Mathematics · tests-for-positive-definiteness

Problem

For what range of numbers

a

and

b

are the matrices

A

and

B

positive definite?

A = \begin{bmatrix} a & 2 & 2 \\ 2 & a & 2 \\ 2 & 2 & a \end{bmatrix} \qquad B = \begin{bmatrix} 1 & 2 & 4 \\ 2 & b & 8 \\ 4 & 8 & 7 \end{bmatrix}.