# How to write the inner product of flatten matrices in a compact form?

I have two matricies which represenet 2D convolutional filters, lets call them $$W_1$$ and $$W_2$$.

I want to make the inner product of the "flattened" versions of these variables to be 0. I.e. $$flatten(W_1)^T flatten(W_2)=0$$.

Is there a compact way to write this expression without using "flatten" funciton where the flatten function returns a columm vector of the matrix.

$$\text{flatten}(A) \cdot \text{flatten}(B) = \langle \text{flatten}(A), \text{flatten}(B) \rangle = \langle A,B \rangle$$
Another common notation is using the trace operator, since $$\langle A, B\rangle = {\rm flatten}(A)^T \cdot {\rm flatten}(B)= {\rm trace}\{A^T B\}$$ for any real-valued $$A, B$$.