Theorems · Theorem · linear algebra

Matrix.toLpLin_mul

∀ {m : Type u_1} {n : Type u_2} {o : Type u_3} {R : Type u_4} [inst : Fintype n] [inst_1 : DecidableEq n]
  [inst_2 : CommRing R] (p q r : ENNReal) [inst_3 : Fintype o] [inst_4 : DecidableEq o] (A : Matrix m n R)
  (B : Matrix n o R), (Matrix.toLpLin p r) (A * B) = (Matrix.toLpLin q r) A ∘ₗ (Matrix.toLpLin p q) B

Note that applying this theorem needs an explicit choice of q.

Defined in

Mathlib.Analysis.Normed.Lp.Matrix

Cited by

2 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeDecidableEqCommRingFintypeDecidableEq