Theorems · Theorem · linear algebra

Module.Basis.coord_toDualEquiv_symm_apply

∀ {R : Type uR} {M : Type uM} {ι : Type uι} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [inst_3 : DecidableEq ι] (b : Module.Basis ι R M) [inst_4 : Finite ι] (i : ι) (f : Module.Dual R M),
  (b.coord i) (b.toDualEquiv.symm f) = (b.dualBasis.coord i) f

Defined in: Mathlib.LinearAlgebra.Dual.Basis
Cited by: 0 results in Mathlib
Foundations: Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring AddCommMonoid Module DecidableEq Finite

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RingHom.idstatement · cited by 18,349
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LinearEquivstatement · cited by 3,317
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Module.Basisstatement and proof · cited by 1,477
LinearEquiv.symmstatement and proof · cited by 1,461
Module.Dualstatement and proof · cited by 583
Module.Basis.reprproof · cited by 498

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