Theorems · Theorem · ring theory
Unitary.spectrum_star_right_conjugate
∀ {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : Ring A] [inst_2 : Algebra R A] [inst_3 : StarMul A]
{a : A} {U : ↥(unitary A)}, spectrum R (↑U * a * star ↑U) = spectrum R aUnitary conjugation preserves the spectrum, star on right.
- Defined in
- Mathlib.Algebra.Star.Unitary
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Ringstatement and proof · cited by 7,463
- Submonoidstatement · cited by 3,086
- Star.starstatement · cited by 1,082
- spectrumstatement · cited by 510
- unitarystatement and proof · cited by 207
- StarMulstatement and proof · cited by 195
- spectrum.units_conjugateproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.IsHermitian.spectrum_eq_image_rangeproof · cited by 1
- Matrix.IsHermitian.spectrum_real_eq_range_eigenvaluesproof · cited by 1
- Unitary.spectrum_star_left_conjugateproof · cited by 0