Linear Algebra and Its Applications · Problem 6.2.15

Positive Definite Matrices — Gilbert Strang

Mathematics · tests-for-positive-definiteness

Problem

Suppose

A

is symmetric positive definite and

Q

is an orthogonal matrix. True or false: (a)

Q^T A Q

is a diagonal matrix. (b)

Q^T A Q

is symmetric positive definite. (c)

Q^T A Q

has the same eigenvalues as

A

. (d)

e^{-A}

is symmetric positive definite.