Talk:Householder transformation

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The applications given feel a bit out of place. Maybe it could be given in the page about tridiagonalization, and link to that here?

orthogonalisation[edit]

If this is an alternative to the Gram-Schmidt process, perhaps this would be a good place for an example and brief discussion of relative merit? Cesiumfrog (talk) 22:40, 23 November 2010 (UTC)

The Householder transformation is mentioned on the Non-Linear Least Squares Method, as well as the QR decomposition page. There should be a link to these pages.. —Preceding unsigned comment added by 187.2.114.212 (talk) 13:27, 30 April 2011 (UTC)

Properties[edit]

This part is VERY poorly explained: "A Householder matrix has eigenvalues \pm 1. To see this, notice that if u is orthogonal to the vector v which was used to create the reflector, then Pu = u, i.e., 1 is an eigenvalue of multiplicity n − 1, since there are n − 1 vectors orthogonal to u. Also, notice Pv = − v, and so -1 is an eigenvalue with multiplicity 1." Nowhere does the writer explain why Pu=u. —Preceding unsigned comment added by 173.248.196.243 (talk) 18:58, 15 February 2011 (UTC)