Theorems · Definition · linear algebra
Matrix.toLpLin
{m : Type u_1} →
{n : Type u_2} →
{R : Type u_4} →
[Fintype n] →
[DecidableEq n] →
[inst : CommRing R] → (p q : ENNReal) → Matrix m n R ≃ₗ[R] WithLp p (n → R) →ₗ[R] WithLp q (m → R)Matrix.toLin' adapted for PiLp R _.
- Defined in
- Mathlib.Analysis.Normed.Lp.Matrix
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEqCommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- ENNRealstatement and proof · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- LinearEquivstatement · cited by 3,317
- LinearEquiv.symmproof · cited by 1,461
- WithLpstatement · cited by 345
- LinearEquiv.transproof · cited by 298
- Matrix.toLin'proof · cited by 86
- WithLp.linearEquivproof · cited by 29
Cited by16
Results whose statement or proof uses this declaration.
- Matrix.toEuclideanLinproof · cited by 22
- Matrix.toLpLinAlgEquivproof · cited by 4
- Matrix.toLpLin_mulstatement · cited by 2
- Matrix.spectrum_toLpLinstatement · cited by 2
- Matrix.toLpLin_onestatement · cited by 1
- Matrix.ofLp_toLpLinstatement · cited by 0
- Matrix.toLpLinAlgEquiv_symm_applystatement · cited by 0
- Matrix.toLpLin_applystatement · cited by 0
- Matrix.toLpLin_eq_toLinstatement · cited by 0
- Matrix.toLpLin_mul_samestatement · cited by 0
- Matrix.toLpLin_powstatement · cited by 0
- Matrix.toLpLin_symm_compstatement and proof · cited by 0