Theorems · Theorem · functional analysis

spectrum.units_conjugate

∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Ring A] [inst_2 : Algebra R A] {a : A} {u : Aˣ},
  spectrum R (↑u * a * ↑u⁻¹) = spectrum R a

Conjugation by a unit preserves the spectrum, inverse on right.

Defined in

Mathlib.Algebra.Algebra.Spectrum.Basic

Cited by

2 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringRingAlgebra