Theorems · Theorem · functional analysis

CStarMatrix.mul_entry_mul_eq_inner_toCLM

∀ {m : Type u_1} {n : Type u_2} {A : Type u_5} [inst : Fintype m] [inst_1 : NonUnitalCStarAlgebra A]
  [inst_2 : PartialOrder A] [inst_3 : StarOrderedRing A] [inst_4 : Fintype n] [inst_5 : DecidableEq m]
  [inst_6 : DecidableEq n] {M : CStarMatrix m n A} {i : m} {j : n} (a b : A),
  a * M i j * star b =
    inner A ((WithCStarModule.equiv A (n → A)).symm (Pi.single j b))
      ((CStarMatrix.toCLM M) ((WithCStarModule.equiv A (m → A)).symm (Pi.single i a)))

Defined in

Mathlib.Analysis.CStarAlgebra.CStarMatrix

Cited by

0 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeNonUnitalCStarAlgebraPartialOrderStarOrderedRingFintypeDecidableEqDecidableEq