Theorems · Theorem · functional analysis
entry_norm_bound_of_unitary
∀ {𝕜 : Type u_1} {n : Type u_3} [inst : RCLike 𝕜] [inst_1 : Fintype n] [inst_2 : DecidableEq n] {U : Matrix n n 𝕜},
U ∈ Matrix.unitaryGroup n 𝕜 → ∀ (i j : n), ‖U i j‖ ≤ 1- Defined in
- Mathlib.Analysis.CStarAlgebra.Matrix
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLikeFintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Norm.normstatement and proof · cited by 5,413
- Finset.sumproof · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- Finset.univproof · cited by 3,473
- Submonoidstatement · cited by 3,086
- RCLikestatement and proof · cited by 2,829
- Finset.sum_congrproof · cited by 2,323
- Multiset.mapproof · cited by 876
- norm_nonnegproof · cited by 725
Cited by1
Results whose statement or proof uses this declaration.
- entrywise_sup_norm_bound_of_unitaryproof · cited by 0