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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


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    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?
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