Theorems · Theorem · group theory

Unitary.tmul_mem

∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] [inst_5 : StarRing A] [inst_6 : StarRing B] [inst_7 : StarRing R]
  [inst_8 : StarModule R A] [inst_9 : StarModule R B] {U : A} {V : B},
  U ∈ unitary A → V ∈ unitary B → U ⊗ₜ[R] V ∈ unitary (TensorProduct R A B)

Defined in

Mathlib.LinearAlgebra.UnitaryGroup

Cited by

0 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebraStarRingStarRingStarRingStarModuleStarModule