Theorems · Theorem · commutative algebra
Algebra.traceMatrix_apply
∀ {κ : Type w} (A : Type u) {B : Type v} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B] (b : κ → B)
(i j : κ), Algebra.traceMatrix A b i j = ((Algebra.traceForm A B) (b i)) (b j)- Defined in
- Mathlib.RingTheory.Trace.Basic
- Cited by
- 3 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- LinearMap.BilinFormstatement · cited by 501
- Algebra.traceFormstatement · cited by 33
- Algebra.traceMatrixstatement · cited by 24
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.traceMatrix_of_basisproof · cited by 2
- Algebra.traceMatrix_of_matrix_vecMulproof · cited by 2
- Rat.numberField_discrproof · cited by 2