Name of special chain matrix product

Question

I often run come across a special chain matrix product $ABA^T$, $A^TBA$ or $ABA^{-1}$, $A^{-1}BA$. Do these operations have a special name?

Answer 1

The common word for this in conjugation, although the use is not entirely standard.

When you conjugate with $A$ and its inverse it is often called similarity.