Theorems · Theorem · commutative algebra
Algebra.traceForm_toMatrix
∀ (R : Type u_1) {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {ι : Type w}
[inst_3 : Fintype ι] [inst_4 : DecidableEq ι] (b : Module.Basis ι R S) (i j : ι),
(LinearMap.BilinForm.toMatrix b) (Algebra.traceForm R S) i j = (Algebra.trace R S) (b i * b j)- Defined in
- Mathlib.RingTheory.Trace.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- LinearEquivstatement · cited by 3,317
- Module.Basisstatement and proof · cited by 1,477
- LinearMap.BilinFormstatement · cited by 501
- Algebra.tracestatement and proof · cited by 90
- LinearMap.BilinForm.toMatrixstatement · cited by 47
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.traceMatrix_of_basisproof · cited by 2
- Algebra.traceForm_toMatrix_powerBasisproof · cited by 0