Linear Algebra and Its Applications · Problem 7.2.16

Computations with Matrices — Gilbert Strang

Mathematics · matrix-norm-qr

Problem

Orthogonal matrices have norm ∥Q∥=1\|Q\| = 1. If A=QRA = QR, show that ∥A∥≤∥R∥\|A\| \leq \|R\| and also ∥R∥≤∥A∥\|R\| \leq \|A\|. Then ∥A∥=∥Q∥∥R∥\|A\| = \|Q\|\|R\|. Find an example of A=LUA = LU with ∥A∥<∥L∥∥U∥\|A\| < \|L\|\|U\|.

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