Changes

: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)

::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)