I have two matricies A and B. A is 3x4, B is 4x4. Right now they are related to a third 4x4 matrix C through an equation in summation notation:

[tex]C_{lk} = \sum_{i=1}^{3 }\sum_{j=1}^{4 }\sum_{m=1}^{4 }B_{kj}B_{lm}A_{ij}A_{im}[/tex]

I'd like to write this in matrix notation, but I'm stumped. My best guess is

[tex]B\times B\times A^T\times A[/tex]

but I tried this with a numerical example, and it doesn't seem to be right. Does anyone know?