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 Dyadics § Double-dot product, 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 A^T:B or A:B^T). —Quondum 16:16, 6 November 2016 (UTC)[reply]

Browsing, I have seen the notations

⟨ A, B ⟩

_F and

⟨ A, B ⟩

, though. —Quondum 03:37, 8 November 2016 (UTC)[reply]

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 Vectorization (mathematics) § Compatibility with inner products. 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)[reply]

Yup, after browsing, the Frobenius inner product seems to be defined as tr(A^HB) or tr(AB^H). 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)[reply]

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)[reply]