Linear Algebra and Its Applications · Problem 7.4.11

Linear Programming and Game Theory — Gilbert Strang

Mathematics · iterative-methods-norm-convergence

Problem

Why is the norm of

B^k

never larger than

\|B\|^k

? Then

\|B\| < 1

guarantees that the powers

B^k

approach zero (convergence). This is no surprise, since

|\lambda|_{\max}

is below

\|B\|