Theorems · Theorem · linear algebra

LinearMap.trace_tensorProduct

∀ (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],
  (TensorProduct.mapBilinear (RingHom.id R) M N M N).compr₂ (LinearMap.trace R (TensorProduct R M N)) =
    (LinearMap.lsmul R R).compl₁₂ (LinearMap.trace R M) (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: CommRing AddCommGroup Module AddCommGroup Module Module.Free Module.Finite Module.Free Module.Finite

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DFunLike.coeproof · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
LinearMapstatement · cited by 10,215
TensorProductstatement and proof · cited by 2,545
TensorProduct.tmulproof · cited by 1,182
Module.Finitestatement and proof · cited by 1,032
LinearMap.extproof · cited by 844
Module.Freestatement and proof · cited by 597
Module.Dualproof · cited by 583

Cited by1

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LinearMap.trace_tensorProduct'proof · cited by 2