Talk:Frobenius inner product

Notation A:B?
I see no support for the notation A:B, given here. Various texts define the Frobenius product, but without this notation in any that I looked at. There is also a conflicting notation at, which is so similar that this may be a confusion of it (they differ by the transpose of either of the multiplicands: using the double-dot product notation, the Frobenius product may be written AT:B or A:BT). —Quondum 16:16, 6 November 2016 (UTC)
 * Browsing, I have seen the notations $⟨A, B⟩$F and $⟨A, B⟩$, though. —Quondum 03:37, 8 November 2016 (UTC)

Hilbert–Schmidt inner product
I see that the Frobenius inner product may be another name for the Hilbert–Schmidt inner product, which would suggest that a redirect to that article is appropriate, with the name Frobenius product being inserted there. As defined here, restricted to real numbers, the two correspond. See here and. Perhaps more generally, on complex numbers, the Frobenius inner product is defined as $tr(AB^{H})$, i.e., identically to the Hilbert–Schmidt inner product? —Quondum 16:54, 6 November 2016 (UTC)
 * Yup, after browsing, the Frobenius inner product seems to be defined as tr(AHB) or tr(ABH). But Hilbert–Schmidt inner product seems to be used in the context of general Hilbert spaces, and Frobenius inner product with real and complex matrices.  So a merge does not seem to be appropriate.  —Quondum 03:31, 8 November 2016 (UTC)


 * I disagree that a merge would not be appropriate. The articles should be merged with mention to the fact that in finite dimensions the Hilbert Schmidt inner product/norms are regularly referred to in the literature as Frobenius inner products/norms. -cbartondock 22:41, 25 April 2018 (UTC)