Can we find Eigenvalues for simultaneous equation?

[wasi-uz-zaman]

hi, please tell me what are the limitations for finding eigenvalues ?
thanks

 

[WannabeNewton]

Could you be more specific? By the fundamental theorem of algebra, there always exists at least one (complex) solution to the characteristic polynomial so there will always be at least one (complex) eigenvalue, where complex means a number of the form $a + bi$.

 

[Jorriss]

Could you be more specific? By the fundamental theorem of algebra, there always exists at least one (complex) solution to the characteristic polynomial so there will always be at least one (complex) eigenvalue, where complex means a number of the form $a + bi$.

Indubitably.

And every finite dimensional real vector space has an invariant subspace of degree one OR two.

 

[micromass]

Could you be more specific? By the fundamental theorem of algebra, there always exists at least one (complex) solution to the characteristic polynomial so there will always be at least one (complex) eigenvalue, where complex means a number of the form $a + bi$.

This is of course only true in the finite-dimensional case.