Talk:Householder transformation

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)[reply]

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)[reply]

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)[reply]

Example section is useless[edit]

I'm currently looking for *any* example of an actual Householder transformation. Sadly not even the Example section on the Wikipedia article of the Householder transformation shows the actual steps of the Householder transformation. The whole section is useless and may very well be removed. 37.120.17.148 (talk) 15:40, 17 November 2015 (UTC)[reply]

Use of inner product[edit]

Can one take the inner product of a point and a vector, $<x,v>$ ? This is written when finding the reflection of $x$ . — Preceding unsigned comment added by Healyp (talk • contribs) 11:16, 31 March 2017 (UTC)[reply]

The part about tridiagonalization[edit]

This is actually about reduction to Hessenberg form, the result of which is tridiagonal if the input matrix A is symmetric. While the process uses Householder reflectors, it uses it in a slightly modified form. There should be a general example about Householder reflectors, not such a specific use-case. Tlkdrt (talk) 21:28, 28 October 2022 (UTC)[reply]