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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

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
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)
The issue, Frank, is that the definition is not only for real spaces - eigenvalues are a property of a linear transformation, which can be performed on any vector space, real, complex, or anything else. If you know anything about this subject, then you're obviously troublemaking, and if you don't, then your edit patterns since returning from your three month block indiciates an attempt to add nonsense.
Frankly, Frank, when a user is blocked for three months a pretty clear message has been sent. Now, obviously, we believe there may still be hope for that editor, or they would have been banned eternally, but don't go around starting stupid fights immediately. I recommend you stay away from math articles - I watch them closely. JacobB 15:35, 2 May 2010 (EDT)
Okay, but could you please change the phrase
  • The determinant is equal to the product of the eigenvalues of a matrix.
into something more correct, like
  • If the characteristic polynom splits into linear factors, then the determinant equals the product of the eigenvalues to the power of their algebraic multiplicity
Thanks, FrankC aka ComedyFan 09:48, 4 May 2010 (EDT)
Well, I changed it myself (see talk:determinant for details) ... FrankC aka ComedyFan 08:50, 5 May 2010 (EDT)