Talk:Eigenvalue

Question about real vs. complex spaces

In the definition, only real spaces are taken into account. So it doesn't make sense to speak of a complex eigenvalue, as for real matrices and real vectors the equation

<math>A\boldsymbol{x}=\lambda\boldsymbol{x}</math>

cannot be solved for a non-real λ (on the left hand side, there will always be a real vector!): only the real roots of the characteristic polynom are eigenvalues!

FrankC aka ComedyFan 14:54, 2 May 2010 (EDT)

Oh, you're back. I don't think you know what you're talking about on this one. JacobB 15:04, 2 May 2010 (EDT

So please, enlighten me. FrankC aka ComedyFan 15:05, 2 May 2010 (EDT)

What are the eigenvalues of the real matrix

<math>\begin{pmatrix}

0 & 1 \\

-1 & 0 \end{pmatrix}</math>.

There aren't any! Of course, you can cheat and embed it in a complex space, but that's a different animal altogether!

FrankC aka ComedyFan 15:17, 2 May 2010 (EDT)