# QR decomposition using Householder transformations

It's been a while since my last post. A project I have in the works requires some matrix decompositions, so I thought this would be a good opportunity to get a post out about QR decompositions using Householder transformations. For the moment we will focus on the field of real numbers, though we can extend these concepts to the complex field if necessary. Theorem. A real matrix, \(\mathbf{A} \in \mathbf{M}_{m,n}\), can be decomposed as \(\mathbf{A}=\mathbf{Q}\mathbf{R}\), where $$\mathbf{Q} Read more [...]