Question

My objective is to start with an “empty” matrix and repeatedly add columns to it until I have a large matrix.

Answer 1

Yes:

>>> a = np.zeros((10, 0))
>>> a.shape
(10, 0)

You can then use ndarray.resize to expand it after the fact without copying. This has some problems though, and for many applications it’ll be easier to use a list of vectors that you then merge into a single array.