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Mathematics

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Algebra

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Algebra - Subfields

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Linear Algebra

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Linear Algebra - Operations/Operators

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Inner Products

Frobenius Inner Product

Created on Jun 22, 2023

Frobenius Inner Product (⟨·,·⟩𝐹)
  • is a type of inner product (⟨·,·⟩) that takes matrices as input
  • is defined as
    • ⟨A,B⟩F​=∑i,j​Aij​​Bij​=Tr(ATB)=Tr(A†B)
    • where the overline denotes the complex conjugate, and † denotes the Hermitian conjugate
  • ⟨·,·⟩𝐹induces a Frobenius Norm (||·||𝐹) defined as: ||·||𝐹 = √(⟨·,·⟩𝐹)