Notations and assumptions
- vector space of dimension . - linear transformation. Denote by for brevity.
The values
Statement
Given the matrix
the expression is a polynomial of degree in .
Therefore, solving
As much as this seems a feasible task for smaller degree polynomials (quadratic or cubic), finding roots of polynomials exactly can be a very hard task (see Abel–Ruffini theorem); at the same time, finding approximations of the roots numerically is relatively easy.