Re: matrices with "repeated eigenvectors"
- From: A N Niel <anniel@xxxxxxxxxxxxxxxxxxxxx>
- Date: Mon, 17 Aug 2009 08:05:06 -0400
In article <h6bglr$nvm$1@xxxxxxxxxxxxxxxxx>, kj <no.email@xxxxxxxxxxx>
wrote:
I know that it is possible for an N x N matrix to lack a set of N
linearly-independent eigenvectors. But I have no intuition at all
for such matrices. Is there a way to characterize them that would
enhance one's intuition? Importantly, is there some type of
situation, or application, where such matrices are common?
And for further reference, is there a compact name for such matrices,
that I could use in a Google search to learn more about them?
TIA!
kynn
Begin by studying the matrix
[0 1]
[0 0]
Figure out why it has no basis of eigenvectors.
Then find "Jordan normal form" in your linear algebra textbook.
By the way, you are talking about "repeated eigenvalues" not "repeated
eigenvectors"
.
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