Theorems · Theorem · linear algebra

Matrix.toLpLin_mul_same

∀ {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 : ENNReal) [inst_3 : Fintype o] [inst_4 : DecidableEq o] (A : Matrix m n R)
  (B : Matrix n o R), (Matrix.toLpLin p p) (A * B) = (Matrix.toLpLin p p) A ∘ₗ (Matrix.toLpLin p p) B

A copy of toLpLin_mul that works for simp, for the common case where the domain and codomain have the same norm.

Defined in

Mathlib.Analysis.Normed.Lp.Matrix

Cited by

0 results in Mathlib

Foundations

Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeDecidableEqCommRingFintypeDecidableEq