Algebraic element

Spectrum of an algebraic element

Let be a K-monoid over and be an algebraic element with minimal polynomial . The roots of are called the eigenvalues of , and the set of all eigenvalues falg

is called the spectrum of .¹ Clearly invertible iff .

Properties

• Spectral mapping theorem

In addition

1. ²

Proof

proof

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tidy | en | sembr

Footnotes

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

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