Linear Algebra and Its Applications · Problem 7.3.6

Computations with Matrices — Gilbert Strang

Mathematics · householder-transformation

Problem

Compute σ=∥x∥\sigma = \|x\|, v=x+σzv = x + \sigma z, and H=I−2vvT/vTvH = I - 2vv^T/v^Tv. Verify Hx=−σzHx = -\sigma z: x=[34]andz=[10].x = \begin{bmatrix} 3 \\ 4 \end{bmatrix} \qquad \text{and} \qquad z = \begin{bmatrix} 1 \\ 0 \end{bmatrix}.

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