Theorems · Theorem · linear algebra
LinearMap.det_pi
∀ {R : Type u_1} [inst : CommRing R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M] {ι : Type u_4}
[inst_3 : Fintype ι] [Module.Free R M] [Module.Finite R M] (f : ι → M →ₗ[R] M),
LinearMap.det (LinearMap.pi fun i => f i ∘ₗ LinearMap.proj i) = ∏ i, LinearMap.det (f i)- Defined in
- Mathlib.LinearAlgebra.Determinant
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites42
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Matrixproof · cited by 4,303
- Equiv.symmproof · cited by 3,681
- MonoidHomstatement · cited by 3,629
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
Cited by2
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.det_piproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasisproof · cited by 1