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To recall, Frobenius product (:) is:

$A:B = trace(A^TB)$

with $A$ and $B$ are matrices.

I don't understand why product rule ($(f.g)'=f'.g+g'.f$) can be used with Frobenius product as well? And what other kinds of product operations that can be used with product rule?

mommomonthewind
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1 Answers1

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There are many so-called products where the product rule works. Take a look at a proof of the product rule, and you can see that most of what's required for that proof to apply is that you can distribute the product over addition, which is kindof required for an operation to deserve the name "product" in the first place.

Arthur
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