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Theorems · Theorem · linear algebra

LinearMap.single_apply

∀ (R : Type u) {ι : Type x} [inst : Semiring R] (φ : ι → Type i) [inst_1 : (i : ι) → AddCommMonoid (φ i)]
  [inst_2 : (i : ι) → Module R (φ i)] [inst_3 : DecidableEq ι] {i : ι} (v : φ i),
  (LinearMap.single R φ i) v = Pi.single i v
Defined in
Mathlib.LinearAlgebra.Pi
Cited by
1 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringAddCommMonoidModuleDecidableEq
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MvPowerSeries.coeff_monomial · cited by 17MvPowerSeries.coeff_monom…DFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidLinearMap · cited by 10215LinearMapPi.single · cited by 518Pi.singleLinearMap.single · cited by 62LinearMap.singleLinearMap.single_applyCITED BYCITES

Cites8

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Cited by1

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