Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Householder matrix Proof

  1. Oct 11, 2009 #1
    I'm working on trying to figure this proof out but its proving to be quite difficult does anyone have any insight?

    Let u and w be vectors in (all real numbers)^n, and let I denote the (n × n) identity matrix. Let A= I + u(w^T), and assume that (w^T)u doesn’t equal -1 (notice that (w^T)u produces a scalar). Prove that
    A^-1= I–au(w^T), where a = 1/(1+(w^T)u)
     
    Last edited: Oct 11, 2009
  2. jcsd
  3. Oct 11, 2009 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    The definition of the inverse of A is B so that AB=BA = Identity

    So if B=I-auwT, what should you do to check that B is the inverse of A?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Householder matrix Proof
Loading...