Frobenius inner product

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In mathematics, the Frobenius inner product is a binary operation that takes two matrices and returns a scalar. It is often denoted ${\displaystyle \langle \mathbf {A} ,\mathbf {B} \rangle _{\mathrm {F} }}$. The operation is a component-wise inner product of two matrices as though they are vectors, and 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.