Theorems · Theorem · functional analysis

CStarMatrix.toCLM_apply_single

∀ {m : Type u_1} {n : Type u_2} {A : Type u_5} [inst : Fintype m] [inst_1 : NonUnitalCStarAlgebra A]
  [inst_2 : DecidableEq m] {M : CStarMatrix m n A} {i : m} (a : A),
  (CStarMatrix.toCLM M) ((WithCStarModule.equiv A (m → A)).symm (Pi.single i a)) =
    (WithCStarModule.equiv A (n → A)).symm fun j => a * M i j

Defined in

Mathlib.Analysis.CStarAlgebra.CStarMatrix

Cited by

2 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeNonUnitalCStarAlgebraDecidableEq