Can array broadcasting treat larger dimensions as smaller numbers?

I am trying to avoid a for loop by using array broadcasting in order to save time.

My setup is as follows: I have a column array of length n where each element is a mxm array (which I'll call A)

and nxm array (which I'll call E)

My end goal is

where each row of this new array is a result of array broadcasting between A_i (a mxm array) and its corresponding row in E (row with t_i).

It seems like the normal array broadcasting rules wouldn't let this happen because technically A is a nmxm array which, I don't believe, can be broadcast with the E since E is nxm. But you could also think of A as a nx1 column where each element of the column is a mxm array, then the dimensions would be within the array broadcasting rules. Is there a way to force this to happen?

Additionally, in my actual code every A_i is the same. Maybe that would make things easier.

To avoid a for loop, reshape E to (n, 1, m) using np.expand_dims(E, axis=1). This allows broadcasting with A, which has the shape (n, m, m). Since every A_i is the same, you can use a single matrix from A for the operation.