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→Issue of complex eigenvalues and eigenvectors
How should we handle the issue of complex eigenvalues and eigenvectors? It's a niche in linear algebra, and perhaps a dubious one at that, but it is in textbooks now.--[[User:Aschlafly|Andy Schlafly]] 19:26, 2 May 2010 (EDT)
How should we handle the issue of complex eigenvalues and eigenvectors? It's a niche in linear algebra, and perhaps a dubious one at that, but it is in textbooks now.--[[User:Aschlafly|Andy Schlafly]] 19:26, 2 May 2010 (EDT)
:My feeling is that we should "proceed formally," as they say. Over any field, we can define a vector space, including the complex field. By limiting our definitions of these concepts to real spaces, we do our readers a disservice. Of course, these are just my thoughts on the matter, and I would be interested to hear your thoughts. [[User:JacobB|JacobB]] 22:27, 2 May 2010 (EDT)
:My feeling is that we should "proceed formally," as they say. Over any field, we can define a vector space, including the complex field. By limiting our definitions of these concepts to real spaces, we do our readers a disservice. Of course, these are just my thoughts on the matter, and I would be interested to hear your thoughts. [[User:JacobB|JacobB]] 22:27, 2 May 2010 (EDT)
::I tried to find a way out of this dilemma: if the characteristic polynomial splits into linear factors (which is always the case for complex spaces, but may not happen for a real space), then the determinant can be calculated using the eigenvalues. But of course, the algebraic multiplicities have to be accounted for. [[User:FrankC|FrankC aka ComedyFan]] 09:07, 5 May 2010 (EDT)