Re: How to find eigenvalue of a matrix in an analytical way?

[CdeMills]

sina2 wrote
> Just days ago, I had to calculate a lot of matrices to find analytical
> eigenvalues. My friend did it on Maple and it worked. Then I tried to find
> it by Octave but it was just in numerical form. I'm curious to know that
> is there anyway to find the eigenvalues in an analytical form?

With the paper and pencil method: eigenvalues are the roots of the
characteristric polynomial; i.e. compute
det(A - lambda I) = 0
where A is a square matrix; lambda is a free variable, and I the identity
matrix with the same size as A.

A=[a11 a12; a21 a22] 
det(A-xI) = (a11-x)(a22-x)-(a12)(a21) 
leads to a second order equation in x whose roots are A eigenvalues.

Regards

Pascal



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