Theorems · Theorem · commutative algebra

Algebra.traceMatrix_eq_embeddingsMatrixReindex_mul_trans

∀ (K : Type u_4) {L : Type u_5} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] {κ : Type w} (E : Type z)
  [inst_3 : Field E] [inst_4 : Algebra K E] [Module.Finite K L] [Algebra.IsSeparable K L] [IsAlgClosed E] (b : κ → L)
  [inst_8 : Fintype κ] (e : κ ≃ (L →ₐ[K] E)),
  (Algebra.traceMatrix K b).map ⇑(algebraMap K E) =
    Algebra.embeddingsMatrixReindex K E b e * (Algebra.embeddingsMatrixReindex K E b e).transpose

Defined in

Mathlib.RingTheory.Trace.Basic

Cited by

2 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebraFieldAlgebraModule.FiniteAlgebra.IsSeparableIsAlgClosedFintype