This page defines every symbol and idea the parent note leans on, from absolute zero. Read it top to bottom — each block only uses words already built above it.
Before any code, picture a row of numbered boxes. Each box holds one number. The label under each box is its index — its position, counting from 0, not 1.
WHY start at 0? Because the index secretly means "how many boxes do I step past the start?" The first box needs zero steps, so it is index 0. Keep that "steps past the start" meaning — it returns when we meet strides.
Look at figure s01: the blue labels on top are the normal indices 0..4; the yellow labels underneath are the negative indices -5..-1. Both point at the same boxes — two names for one address.
The parent note says an array is "numbers laid out in memory, plus a recipe (shape + strides)." Let's earn every word of that.
WHY does NumPy bother with a separate recipe instead of just a list? Because the actual numbers sit in one flat strip of memory. The recipe reinterprets that flat strip as a row, a grid, or a cube — without moving a single number. That single fact is the seed of "view vs copy" later. See NumPy arrays — shape, strides, dtype.
In figure s02: the bottom bar is the flat memory strip (the real data). The top grid is what you see as a 3×4 array. The arrows show that "move one column right" = step 1 in memory, but "move one row down" = step 4 in memory (skip a whole row). Those step-sizes are the strides.
The parent's first tool is a[start:stop:step]. Three new symbols hide in there: the colon, and the three numbers around it.
WHY is stopexcluded? Because of the "steps past the start" meaning of an index: start up to but not includingstop makes the length come out as a clean subtraction, stop - start (when step=1). No off-by-one bookkeeping.
Figure s03 walks a[1:8:2]: green ring on box 1 (start), red stop-line just before box 8 (never taken), yellow jumps of size 2. Collected boxes: 1, 3, 5, 7.
The parent writes A[1, 2] and A[0:2, 1:3]. The comma is the new symbol.
WHY do we need it? A grid has two independent addresses. Without the comma NumPy couldn't tell "row 1" from "column 1". Each slot between commas can itself be a single index or a full start:stop:step slice.
Recall Why
A[:, -1] is the last column
: on the left = all rows. -1 on the right = last column. Together: the last column of every row.
Answer ::: it grabs index -1 (last box) from every single row, giving one value per row.
Section 2 of the parent uses a boolean array. New idea: a value that is only ever True or False.
WHY does the topic need booleans? Because a condition like "is this number positive?" answers yes or no for each box. Collect those answers and you get a stencil telling NumPy which boxes to keep.
Figure s04: top row is the data, middle row is the boolean stencil made by a > 0 (green ✓ = True, red ✗ = False), bottom is what "falls through the holes" — the kept values, gathered into a new shorter strip.
Section 3 passes a[[i0, i1, i2]] — a list of integers. New symbols: the inner square brackets [...] and the idea of a position list.
WHY allow a list of positions when we already have slices? Because a slice can only walk in a regular rhythm (fixed step). A list can pick boxes in any order and even repeat them — things a rhythm can never do. That is the whole point of fancy indexing.
Now that "recipe" and "flat strip" exist, the parent's headline distinction is easy.
WHY does a slice give a view but a mask/list gives a copy? A slice keeps a regular rhythm, so a single start + step recipe still describes it — no numbers need moving. A mask or list picks boxes scattered irregularly; no single rhythm can describe them, so NumPy must gather them into a fresh strip. See Views vs Copies — memory model.
The topic sits at the bottom because it needs every foundation above it. Missing any one is where beginners get stuck. Related deeper notes: Broadcasting, Vectorization — replacing Python loops, np.where and conditional selection, Pandas .loc / .iloc indexing, and the parent indexing overview.
