Theorems · Theorem · functional analysis
CStarMatrix.toCLM_apply
∀ {m : Type u_1} {n : Type u_2} {A : Type u_5} [inst : Fintype m] [inst_1 : NonUnitalCStarAlgebra A]
{M : CStarMatrix m n A} {v : WithCStarModule A (m → A)},
(CStarMatrix.toCLM M) v = (WithCStarModule.equiv A (n → A)).symm (Matrix.vecMul v M)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeNonUnitalCStarAlgebra
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- LinearMapstatement · cited by 10,215
- Equivstatement · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Complexstatement · cited by 5,565
- ContinuousLinearMapstatement · cited by 5,352
- Equiv.symmstatement · cited by 3,681
- NonUnitalCStarAlgebrastatement and proof · cited by 149
- Matrix.vecMulstatement · cited by 148
- CStarMatrixstatement and proof · cited by 67
- WithCStarModulestatement and proof · cited by 66
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