Theorems · Theorem · field theory
Algebra.normalizedTrace_eq_of_finiteDimensional_apply
∀ (F : Type u_1) {K : Type u_2} [inst : Field F] [inst_1 : Field K] [inst_2 : Algebra F K] [inst_3 : CharZero F]
[inst_4 : Algebra.IsIntegral F K] [FiniteDimensional F K] (a : K),
(Algebra.normalizedTrace F K) a = (↑(Module.finrank F K))⁻¹ • (Algebra.trace F K) a- Defined in
- Mathlib.FieldTheory.NormalizedTrace
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- Fieldstatement and proof · cited by 7,404
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement · cited by 1,770
- CharZerostatement and proof · cited by 932
- Algebra.IsIntegralstatement and proof · cited by 224
- Algebra.tracestatement · cited by 90
- Algebra.normalizedTracestatement · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.normalizedTrace_eq_of_finiteDimensionalproof · cited by 0