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How should I get symbolic expression of eigenvalues and eigenvectors of a real symmetric matrix 3x3

asked 2014-02-16 20:24:10 +0200

Jon gravatar image

updated 2014-02-17 02:35:24 +0200

slelievre gravatar image

Hi all I am a physicist and a new user of Sage. I used the following command on "Sage Version 5.1, Release Date: 2012-07-09", to get the expression of eigenvalue and eigenvectors of the symmetric real 3x3 matrix.


It seems that this type of expression is unavailable, as it took forever to calculate on my laptop (Intel core i7) . So I would like to ask if I used the wrong command or mathematically the analytical expression is unavailable. Thanks very much.

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answered 2014-02-17 02:48:37 +0200

slelievre gravatar image

updated 2014-02-17 02:59:11 +0200

You can access the documentation for eigenvalues_right:

sage: gamma.eigenvectors_right?

or the source code:

sage: gamma.eigenvectors_right??

There you see that the right eigenvectors are computed by computing the left eigenvectors of the transpose matrix. So let's check the documentation for eigenvectors_left:

sage: gamma.eigenvectors_left?

or the source code:

sage: gamma.eigenvectors_left??

You can see there an example involving a 2x2 matrix with symbolic entries, followed by the following comment:

This routine calls Maxima and can struggle with even small matrices
with a few variables, such as a `3\times 3` matrix with three variables.
However, if the entries are integers or rationals it can produce exact
values in a reasonable time.

Note: to get the documentation for that command in html format, do:

sage: browse_sage_doc(gamma.eigenvectors_left)
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Asked: 2014-02-16 20:24:10 +0200

Seen: 1,592 times

Last updated: Feb 17 '14