Theorems · Theorem · ring theory
Unitary.spectrum_star_left_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 (star ↑U * a * ↑U) = spectrum R aUnitary conjugation preserves the spectrum, star on left.
- Defined in
- Mathlib.Algebra.Star.Unitary
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
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- 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 and proof · cited by 1,082
- spectrumstatement and proof · cited by 510
- unitarystatement and proof · cited by 207
- StarMulstatement and proof · cited by 195
- star_starproof · cited by 135
- Unitary.spectrum_star_right_conjugateproof · cited by 3
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