Jul 10, 2017 · For $\Bbb R^n$, Householder matrix $Q=I-2vv^T$ is an operator that maps a vector to its reflection across a hyperplane of normal $v$.

What is the Householder matrix for complex vector space? 1. Eigendecomposition of Householder matrix. 0.

A Householder matrix $H = I - c u u^T$, where $c$ is a constant and $u$ is a unit vector, always comes out orthogonal and full rank.

Sep 25, 2013 · I understand that a householder matrix has eigenvalues of either 1 or -1, however I isn't clear to me why the determinant is -1. Clearly the determinant is equal to the product of …

Jul 1, 2015 · Householder matrices are orthogonal and symmetric. That is: $$ (I - 2uu^T)^T = I - 2uu^T $$ $$ (I - 2uu^T)^2 = I - 4uu^T + 4u(u^Tu)u^T = I $$

Apr 20, 2020 · Q*R gives A (at least for your matrix A). Having different Q and R from MATLAB's implementation does not necessarily mean something is wrong (as long as Q*R=A and Q is …

Oct 27, 2020 · A Householder matrix as a product of Givens matrices. Ask Question Asked 4 years, 4 months ago.

You can always use the Householder method to tridiagonalize a matrix. Basically the Householder transformation is doing this: I think it is the best if you write where you started with the …

Aug 13, 2020 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …

Dec 15, 2021 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …