Theorems · Theorem · linear algebra

LinearMap.trace_eq_matrix_trace

∀ (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] (b : Module.Basis ι R M) (f : M →ₗ[R] M),
  (LinearMap.trace R M) f = ((LinearMap.toMatrix b b) f).trace

Defined in

Mathlib.LinearAlgebra.Trace

Cited by

14 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleDecidableEqFintype