Algebraic element

Spectrum of an algebraic element

Let be a -monoid over and be an algebraic element with minimal polynomial . The roots of are called the eigenvalues of , and the set of all eigenvalues #m/def/ralg

is called the spectrum of .1 Clearly invertible iff .

Properties

In addition

  1. 2
Proof

#missing/proof


#state/tidy | #lang/en | #SemBr

Footnotes

  1. 2008. Advanced Linear Algebra, §18, p. 461

  2. Stated with partial proof in 2008. Advanced Linear Algebra, §18, p. 462