Eigenvector result is unusual
06-24-2014, 12:52 AM (This post was last modified: 06-24-2014 01:14 AM by Rich.)
Post: #1
 Rich Junior Member Posts: 47 Joined: Jan 2014
Eigenvector result is unusual
Hi,

When i type in

EIGENVV([1,2],[4,3])

I get this result:

{[[0.4472135955,−0.7453559925],[0.894427191,0.7453559925]],[[5.,0],[0,-1.]]}

I am not sure if my math is wrong somewhere, but on paper i get the different eigenvalues, for 5, i get [1 2] and for -1, I get [1 -1] which is what wolfram alpha gets. My 50G gets a value of [.5 1] and [1 -1] for for 5 and -1 respectively. Which is also correct.

EDIT::: Actually looking a little past the abstract, the results are correct, but I am not sure why the HP Prime didn't come up with a number closer to a whole number or more readable output similar to the 50G.
06-24-2014, 01:28 AM
Post: #2
 Helge Gabert Senior Member Posts: 467 Joined: Dec 2013
RE: Eigenvector result is unusual
I don't think the math is wrong.

The eigenvalues of lambda1 and lambda2 are correct (5, and -1), and this is also what Wolfram alpha shows.

The eigenvectors are [.44..., .89...], and multiplied by a suitable scaling factor equals [1,2], and ditto for the other eigenvector [-.74..., .74], which, again, multiplied with a suitable scaling factor equals [-1,1] - - again in agreement with Wolfram alpha. I believe you read the vectors the wrong way - - horizontally instead of vertically.

But we can ask - - why doesn't the Prime normalize the eigenvectors?
06-24-2014, 01:39 AM (This post was last modified: 06-24-2014 01:40 AM by Rich.)
Post: #3
 Rich Junior Member Posts: 47 Joined: Jan 2014
RE: Eigenvector result is unusual
Thanks for the update, I was reading it wrong. I noticed that it when diagonalizing the matrix on the Prime, with those eigenvectors, it still gives me the correct result but instead of a zeros, it has -1.42109E-15, which is essentially zero... but maybe due to the original output.
06-24-2014, 05:27 AM
Post: #4
 parisse Senior Member Posts: 1,236 Joined: Dec 2013
RE: Eigenvector result is unusual
EIGENVV is an approx instruction. Try an exact one, for example jordan.
06-24-2014, 11:41 AM
Post: #5
 Rich Junior Member Posts: 47 Joined: Jan 2014
RE: Eigenvector result is unusual
Thank you, the Jordan function works perfectly.
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