Making arrays

You'll rarely type an array out by hand. Nearly every array starts as one of a handful of constructors, and they all follow the same pattern: choose a shape, then choose how to fill it.

np.zeros(shape) and np.ones(shape) are the workhorses. Note the double brackets in np.zeros((3, 4)) — the shape is a single tuple argument, not two separate ones. Forgetting that is the most common first-day error with these.

Both give you float64. If you wanted integers, say so: np.zeros((3, 4), dtype=int).

arange and linspace

These two look similar and answer different questions. np.arange(0, 10, 2) takes a step and, like Python's range, excludes the stop. np.linspace(0, 10, 5) takes a count and includes both ends.

np.arange(0, 10, 2)     # [0 2 4 6 8]        — stop excluded
np.linspace(0, 10, 5)   # [0. 2.5 5. 7.5 10.] — both ends included

Reach for linspace whenever you know how many points you want — plotting a smooth curve, sampling a range evenly. Reach for arange when you care about the gap between values. And avoid arange with a float step: floating-point drift means you can't reliably predict how many elements you'll get.

Random numbers

Modern NumPy wants you to make a generator first:

rng = np.random.default_rng(0)   # 0 is the seed
rng.random((3, 4))               # floats in [0, 1)
rng.integers(0, 10, size=(3, 4)) # ints in [0, 10)
rng.normal(size=5)               # standard normal

You'll still see the older np.random.rand style in tutorials; it works, but the generator form is the one to learn. Passing a seed makes the output reproducible — the same numbers every run, which is exactly what you want in a lesson, a test, or anything you plan to debug.