What does (n,) mean in the context of numpy and vectors?
(n,) is a tuple of length 1, whose only element is n. (The syntax isn't (n) because that's just n instead of making a tuple.)
If an array has shape (n,), that means it's a 1-dimensional array with a length of n along its only dimension. It's not a row vector or a column vector; it doesn't have rows or columns. It's just a vector.
I've tried searching StackOverflow, googling, and even using symbolhound to do character searches, but was unable to find an answer. Specifically, I'm confused about Ch. 1 of Nielsen's Neural Networks and Deep Learning, where he says "It is assumed that the input a is an (n, 1) Numpy ndarray, not a (n,) vector."
At first I thought (n,) referred to the orientation of the array - so it might refer to a one-column vector as opposed to a vector with only one row. But then I don't see why we need (n,) and (n, 1) both - they seem to say the same thing. I know I'm misunderstanding something but am unsure.
For reference a refers to a vector of activations that will be input to a given layer of a neural network, before being transformed by the weights and biases to produce the output vector of activations for the next layer.
EDIT: This question equivocates between a "one-column vector" (there's no such thing) and a "one-column matrix" (does actually exist). Same for "one-row vector" and "one-row matrix". 
A vector is only a list of numbers, or (equivalently) a list of scalar transformations on the basis vectors of a vector space. A vector might look like a matrix when we write it out, if it only has one row (or one column). Confusingly, we will sometimes refer to a "vector of activations" but actually mean "a single-row matrix of activation values transposed so that it is a single-column."
Be aware that in neither case are we discussing a one-dimensional vector, which would be a vector defined by only one number (unless, trivially, n==1, in which case the concept of a "column" or "row" distinction would be meaningless).