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Created page with '== Question about real vs. comples spaces == In the definition, only ''real'' spaces are taken into account. So it doesn't make sense to speak of a ''complex'' eigenvalue, as fo…'
== Question about real vs. comples 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!
[[User:FrankC|FrankC aka ComedyFan]] 14:54, 2 May 2010 (EDT)
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!
[[User:FrankC|FrankC aka ComedyFan]] 14:54, 2 May 2010 (EDT)