How do I create an empty array/matrix in NumPy?

You have the wrong mental model for using NumPy efficiently. NumPy arrays are stored in contiguous blocks of memory. If you want to add rows or columns to an existing array, the entire array needs to be copied to a new block of memory, creating gaps for the new elements to be stored. This is very inefficient if done repeatedly to build an array.

In the case of adding rows, your best bet is to create an array that is as big as your data set will eventually be, and then assign data to it row-by-row:

>>> import numpy
>>> a = numpy.zeros(shape=(5,2))
>>> a
array([[ 0.,  0.],
   [ 0.,  0.],
   [ 0.,  0.],
   [ 0.,  0.],
   [ 0.,  0.]])
>>> a[0] = [1,2]
>>> a[1] = [2,3]
>>> a
array([[ 1.,  2.],
   [ 2.,  3.],
   [ 0.,  0.],
   [ 0.,  0.],
   [ 0.,  0.]])