Theorems · Theorem · functional analysis
entrywise_sup_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 → ‖U‖ ≤ 1The entrywise sup norm of a unitary matrix is at most 1.
- Defined in
- Mathlib.Analysis.CStarAlgebra.Matrix
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLikeFintypeDecidableEq
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- Realstatement · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Norm.normstatement · cited by 5,413
- Matrixstatement and proof · cited by 4,303
- Submonoidstatement · cited by 3,086
- RCLikestatement and proof · cited by 2,829
- SeminormedAddGroupproof · cited by 331
- zero_le_oneproof · cited by 316
- Matrix.unitaryGroupstatement and proof · cited by 37
- pi_norm_le_iff_of_nonnegproof · cited by 18
- entry_norm_bound_of_unitaryproof · cited by 1
- Matrix.normedAddCommGroupstatement · cited by 1
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