What does multiplying a matrix A by B and B transpose mean?

208 Views Asked by At

$$BA^TB^T$$

$A$ is ($m\times m$) while $B$ is ($n\times m$). In matlab this is written as: B*(A\B').

I don't understand what it means for $A$. What kind of transformation does it do on $A$? What does the result of this represent?

edit:

I've been asked to explain what I mean but what I am asking myself is what the result an expression like this yields. In a linear system

 Ax = b

I understand what x= inverse(A)*b means. It solves the system. But if A and B are both matrices and not vectors what does it do? And when that solution is again multiplied by the matrix b to form $$BA^TB^T$$
what does that expression mean? What is the transformation it effects. I've explained my question as best as I could, I think you understand what I'm asking. I'd very much like to read your answers.

edit #2: For the original expression, I will provide some context as to where I have encountered it. It is used in a FETI-DP method and A is the original matrix reordered per domain and B is a matrix of connections of interface nodes in different domains. I hope this helps make it clearer.