Theorems · Theorem · linear algebra

Matrix.trace_toLin_eq

∀ {R : Type u} [inst : CommSemiring R] {M : Type v} [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Type w}
  [inst_3 : DecidableEq ι] [inst_4 : Fintype ι] (A : Matrix ι ι R) (b : Module.Basis ι R M),
  (LinearMap.trace R M) ((Matrix.toLin b b) A) = A.trace

Defined in

Mathlib.LinearAlgebra.Trace

Cited by

1 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleDecidableEqFintype