Ask Your Question
0

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

asked 2014-02-16 13:24:10 -0500

Jon gravatar image

updated 2014-02-16 19:35:24 -0500

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.

var('g11,g12,g13,g22,g23,g33',domain='real')
gamma=matrix(3,3,[g11,g12,g13,g12,g22,g23,g13,g23,g33])
eigs=gamma.eigenvectors_right()

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.

edit retag flag offensive close merge delete

1 answer

Sort by » oldest newest most voted
0

answered 2014-02-16 19:48:37 -0500

updated 2014-02-16 19:59:11 -0500

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)
edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

Stats

Asked: 2014-02-16 13:24:10 -0500

Seen: 693 times

Last updated: Feb 16 '14