Theorems · Theorem · linear algebra
Matrix.permMatrix_l2_opNorm_le
∀ {n : Type u_1} [inst : DecidableEq n] (σ : Equiv.Perm n) [inst_1 : Fintype n] {𝕜 : Type u_3} [inst_2 : RCLike 𝕜],
‖Equiv.Perm.permMatrix 𝕜 σ‖ ≤ 1The l2-operator norm of a permutation matrix is bounded above by 1.
See Matrix.permMatrix_l2_opNorm_eq for the equality statement assuming the matrix is nonempty.
- Defined in
- Mathlib.LinearAlgebra.Matrix.Permutation
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 238 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintypeRCLike
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 · cited by 25,697
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Set.ofPredproof · cited by 6,101
- Norm.normstatement and proof · cited by 5,413
- Finset.sumproof · cited by 5,195
- Matrixstatement · cited by 4,303
- Finset.univproof · cited by 3,473
- one_mulproof · cited by 2,841
- RCLikestatement and proof · cited by 2,829
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.permMatrix_l2_opNorm_eqproof · cited by 0
- Matrix.l2_opNorm_le_one_of_mem_doublyStochasticproof · cited by 0