I'm looking for a name for the following, frequently recurring, product. Or better said: curious whether such a name or names exist.
"A times B times (A transposed)"
Where A and B can be matrices, but it also comes in similar forms with vectors and quaternions:
"Q times V times (Q conjugated)"
Since it's hard to look for something you don't know how to call (unless google has a mathematical symbolical search feature that I haven't discovered yet...) I'm hoping to share in your knowledge.
Note that my interest is more of a curiosity than a quest for the one truth, since I well aware naming convention as notation conventions can differ from field to field and even person to person.
Regards,
Rouke
The ABA^T case is covered here (that's "congruence transformation"). For transformations with orthogonal matrices / unit quaternions (where A^T equals A^{-1}, and conj(Q) equals Q^{-1}), this is also equivalent to ABA^{-1}, which you can read about here.