Linear Algebra and Its Applications · Problem 7.2.3

Computations with Matrices — Gilbert Strang

Mathematics · matrix-norm-condition-number

Problem

Explain why ∥ABx∥≤∥A∥∥B∥∥x∥\|ABx\| \leq \|A\|\|B\|\|x\|, and deduce from equation (5) that ∥AB∥≤∥A∥∥B∥\|AB\| \leq \|A\|\|B\|. Show that this also implies c(AB)≤c(A)c(B)c(AB) \leq c(A)c(B).

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