Re: Is this matrix diagonalizable?

On 2007-09-30 13:10:57 -0400, "Carl R." <solrac140@xxxxxxxxxxx> said:

Hello

Let A = [1 3 1 2 ]
[0 -1 1 3]
[0 0 2 5]
[0 0 0 -2]

The characteristic equation is
det (tI - A) = (t-1)(t+1)(t-2)(t+2).

I see 4 distinct eigenvalues.


So I found that we have two repeated eigenvalues, namely lambda = 2.
Therefore among the 4 eigenvectors there are two eigenvectors which
have the same value, hence they can't
be linearly independent because a vector is a multiple of itself.
Therefore A is not diagonalizable. Is this correct?
Is there another way to see it?

Thanks in advance


--

-kira

.

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