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.

 

[pmacias]

for your question. The answer is yes, it is possible to find eigenvalues for simultaneous equations. However, there are some limitations to this approach. One limitation is that eigenvalues can only be found for square matrices, meaning that the number of equations must be equal to the number of variables. Additionally, the equations must be linear and independent. If these conditions are not met, then the eigenvalues cannot be calculated. Another limitation is that eigenvalues can only be found for certain types of matrices, such as symmetric or diagonal matrices. Finally, the eigenvalues may not always be unique, meaning that there can be multiple sets of eigenvalues for a given system of equations. Overall, while finding eigenvalues for simultaneous equations can be a useful tool in certain situations, it is important to be aware of these limitations and to consider other methods for solving simultaneous equations when necessary.