Linear Algebra and Its Applications · Problem 7.3.5

Computations with Matrices — Gilbert Strang

Mathematics · householder-transformation

Problem

Show that for any two different vectors of the same length, ∥x∥=∥y∥\|x\| = \|y\|, the Householder transformation with v=x−yv = x - y gives Hx=yHx = y and Hy=xHy = x.

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