How to use QR decomposition to find eigenvalues?

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QR decomposition can be used to find eigenvalues through an iterative process involving the factorization of a matrix into an orthogonal matrix Q and an upper triangular matrix R. The method involves repeatedly applying QR decomposition to the matrix and updating it with the product RQ. This iterative approach converges to a form where the eigenvalues can be extracted from the diagonal elements of the resulting matrix. It is important to note that the eigenvalues obtained are approximations of the true values. Understanding the iterative nature of this method is crucial for effectively using QR decomposition to find eigenvalues.
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Homework Statement


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.


Homework Equations



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

The Attempt at a Solution



det(λ*I - QR) = 0? this doesn't really help.
 
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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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