[jampekka]

Broadcasting is an excellent idea. Implementations do have warts, but e.g. pytorch would be really painful without it.

Broadcasting is a sort of generalization of the idea of scalar-matrix product. You could make that less "ridiculous" by requiring a Hadamard product with a constant value matrix instead.

[bee_rider]

Scalar-matrix multiplication doesn’t seem that weird; automatically converting a 1x1 matrix to a scalar is the weird seeming thing, IMO.