Theorems · Theorem · linear algebra

LinearMap.trace_prodMap

∀ (R : Type u_1) [inst : CommRing R] (M : Type u_2) [inst_1 : AddCommGroup M] [inst_2 : Module R M] (N : Type u_3)
  [inst_3 : AddCommGroup N] [inst_4 : Module R N] [Module.Free R M] [Module.Finite R M] [Module.Free R N]
  [Module.Finite R N],
  LinearMap.trace R (M × N) ∘ₗ LinearMap.prodMapLinear R M N M N R =
    LinearMap.id.coprod LinearMap.id ∘ₗ (LinearMap.trace R M).prodMap (LinearMap.trace R N)

Defined in

Mathlib.LinearAlgebra.Trace

Cited by

1 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleModule.FreeModule.FiniteModule.FreeModule.Finite