Terminology: $\mathbf{A} \mathbf{B} \mathbf{A}^T$ What is this operation called in linear algebra:
$$
\mathbf{A} \mathbf{B} \mathbf{A}^T
$$
EDIT: I'm particularly interested in terminology as it applies to the Extended Kalman Filter which has these two steps involving the above operation:
$$
{\boldsymbol  {P}}_{{k|k-1}}={{{{\boldsymbol  {F}}_{{k-1}}}}}{{\boldsymbol  {P}}_{{k-1|k-1}}}{{{{\boldsymbol  {F}}_{{k-1}}^{\top }}}}{+}{{\boldsymbol  {L}}_{{k-1}}}{{\boldsymbol  {Q}}_{{k-1}}}{{\boldsymbol  {L}}_{{k-1}}^{{T}}}
$$
$$
{\boldsymbol  {S}}_{{k}}={{{\boldsymbol  {H}}_{{k}}}}{{\boldsymbol  {P}}_{{k|k-1}}}{{{\boldsymbol  {H}}_{{k}}^{\top }}}{+}{{\boldsymbol  {M}}_{{k}}}{{\boldsymbol  {R}}_{{k}}}{{\boldsymbol  {M}}_{{k}}^{{T}}}
$$
 A: For general matrices, especially not necessarily square, the only structural sense of this is evaluation of a quadratic form attached to $B$ on the rows of $A$.
There surely are various more-or-less classical terms for this and other operations on matrices ... which mostly do not give any clue, from the language used, about the structural or operational significance. Maybe better to not hunt these usages down and resurrect them.
That is, in contrast, $ABA^{-1}$ with square matrices is change-of-coordinates (a.k.a. "conjugation") for the linear map given by $B$.
For square matrices, $ABA^\top$ or $A^\top BA$ is change-of-coordinates for the quadratic form given by $B$. 
For non-square $A$, the only obvious structural/operational sense of $ABA^\top$ or $A^\top BA$ is as producing the matrix of quadratic form/inner product values for the rows/columns of $A$ for the quadratic form $B$. 
Seriously, although I know there are antique English-language and other words for these operations, they are almost entirely inferior to less coordinate-referent naming conventions.
A: $B\mapsto A^TBA$ is called matrix congruence and arises in the change of basis of a quadratic form represented by matrix $B$.
A: It's a kind of conjugation. I don't think there's a completely standard name for it. 
