Linear Algebra and Its Applications · Problem 7.2.9

Computations with Matrices — Gilbert Strang

Mathematics · matrix-norm

Problem

Show that

\max|\lambda|

is not a true norm, by finding 2 by 2 counterexamples to

\lambda_{\max}(A+B) \leq \lambda_{\max}(A) + \lambda_{\max}(B)

and

\lambda_{\max}(AB) \leq \lambda_{\max}(A)\lambda_{\max}(B)