Theorems · Theorem · linear algebra

LinearMap.trace_eq_matrix_trace_of_finset

∀ (R : Type u) [inst : CommSemiring R] {M : Type v} [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {s : Finset M}
  (b : Module.Basis (↥s) R M) (f : M →ₗ[R] M), (LinearMap.trace R M) f = ((LinearMap.toMatrix b b) f).trace

Auxiliary lemma for trace_eq_matrix_trace.

Defined in

Mathlib.LinearAlgebra.Trace

Cited by

1 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModule