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How to use QR decomposition to find eigenvalues?

  1. Nov 30, 2013 #1
    1. The problem statement, all variables and given/known data
    I need to understand how I would go about using QR decomposition of a matrix to find the matrix's eigenvalues. I know how to find the factorization, just stuck on how I would use that factorization to find the eigenvalues.

    2. Relevant equations

    A=QR where Q is an orthogonal matrix such that Qtranspose = Qinverse

    3. The attempt at a solution

    det(λ*I - QR) = 0? this doesn't really help.
  2. jcsd
  3. Nov 30, 2013 #2


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    If you do a google search, you will find a number of different hits on this topic.

    Here is one such hit: http://www.mcs.csueastbay.edu/~malek/TeX/Qr.pdf

    The use of QR for finding eigenvalues is iterative, however. The values returned are approximations of the true eigenvalues.
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