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Frobenius inner product
Binary operation, takes two matrices and returns a scalar
Frobenius inner product
In mathematics, the Frobenius inner product (also known as the double-dot product) is a binary operation that takes two matrices and returns a scalar. It is often denoted ⟨ A , B ⟩ F {\displaystyle \langle \mathbf {A} ,\mathbf {B} \rangle _{\mathrm {F} }} or A : B {\displaystyle \mathbf {A} :\mathbf {B} } . The operation is the inner product of two matrices as though their entries were the components of vectors, and it satisfies the axioms for an inner product. The two matrices must have the same dimension—same number of rows and columns—but are not restricted to be square matrices. It is named after Ferdinand Georg Frobenius.
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