Theorems · Theorem · linear algebra
Algebra.det_lsmul
∀ {R : Type u_5} {S : Type u_6} [inst : CommRing R] [inst_1 : Ring S] [inst_2 : Algebra R S] [Module.Free R S] (x : R),
LinearMap.det ((Algebra.lsmul R R S) x) = x ^ Module.finrank R S- Defined in
- Mathlib.LinearAlgebra.Determinant
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- mul_oneproof · cited by 3,885
- MonoidHomstatement · cited by 3,629
- AlgHomstatement · cited by 3,236
- Module.finrankstatement and proof · cited by 1,770
- map_oneproof · cited by 861
- Module.Endstatement and proof · cited by 774
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.norm_algebraMapproof · cited by 13