Eigenvalues are correct

JacquesC — Sun, 18 Feb 2007 08:20:27 Z

The eigenvalues returned are complex. For theta real, cos(theta)^2-1 is negative, so its square root is usually complex. The Eigenvectors are quite complicated, since they depend on whether sin(theta)

Pen and Paper

dcasimir — Sun, 18 Feb 2007 22:21:46 Z

Does that mean I can only find these eigenvectors by hand ?

Thanks, A Lot to Digest

dcasimir — Mon, 19 Feb 2007 02:48:31 Z

Thanks, I'll admit I didn't get it on the first reading, but it gives me something to mull over for awhile and possibly help with my understanding. v/r, Dan

A way to coax the eigenvectors out

Alex Smith — Mon, 19 Feb 2007 03:05:36 Z

Try asking Maple for the eigenvectors of this matrix: M:=Matrix([[c,-sqrt(1-c^2)],[sqrt(1-c^2),c]]); Eigenvectors(M,output=list); Then put c=cos(theta). This seems to give a fairly general form.

How Do I Substitute In the Cosine Function ?

dcasimir — Tue, 20 Feb 2007 07:21:34 Z

Thanks. Another question. How would I put the cosine function into the Eigenvectors output, that contains "RootOf" expressions ? would the "op" or "subsop" operator be useful ?

eval or subs

Doug Meade — Tue, 20 Feb 2007 08:04:22 Z

I would use eval, as follows:

eval( MyExpression, c=cos(theta) );

You could use subs, with the syntax:

subs( c=cos(theta), MyExpression );

There are some minor technical differences, but I find the eval fits my usage best. A third option is to create a function, with unapply as follows:

MyFunction := unapply( MyExpression, c );
MyFunction( cos(theta) );

I hope this is useful, Doug