OAI/LinearAlgebra/MatrixMultiplication/AuxiliarySeparation/Tensor/BinaryCharacter.lean

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1 declarations, 0 contain sorry, 0 declared as axioms

Character additivity for binary tensor sums

The summands may have different finite coordinate types. A binary sum is a coordinate reindexing of the dependent direct sum over Bool.

  1. theorem OAI.MatrixMultiplication.AuxiliarySeparation.Character.value_sumTensor line 22

    Source documentation

    A character is additive on binary direct sums with arbitrary finite coordinate types.

    theorem value_sumTensor (χ : Character)
        {X Y Z U V W : Type}
        [Fintype X] [Fintype Y] [Fintype Z]
        [Fintype U] [Fintype V] [Fintype W]
        (T : Tensor ℂ X Y Z) (S : Tensor ℂ U V W) :
        χ.value (sumTensor T S) = χ.value T + χ.value S := by
    …

    Mentions: OAI.MatrixMultiplication.AuxiliarySeparation.Character, OAI.MatrixMultiplication.AuxiliarySeparation.sumTensor