2D Slicing: Rows, Columns & Sub-matrices

"All players' scores in match 1", "the first two players", "Virat and Rohit in matches 1–4" — each of these is a rectangular piece of the scores table. In NumPy you cut such pieces by putting a slice on each axis.

Definition

2D slicing selects a rectangular region of a 2D array by giving a slice (or index) for each axis: arr[row_slice, col_slice]. Each slice follows the usual start:stop:step rules, and a bare colon : means "every position on this axis". The result is a view of the original array.

• Slice per axis — rows and columns are sliced independently; arr[0:2, 0:4] means rows 0–1 and columns 0–3.
• Bare colon : — "take all rows" or "take all columns".
• Index vs slice on an axis — an integer removes that axis (result has fewer dimensions); a slice keeps it, even if it selects only one position.
• View — no data is copied; editing the result edits scores.

Syntax

arr[r1:r2, c1:c2]   # sub-matrix: rows r1..r2-1, columns c1..c2-1
arr[:, c]           # column c (1D)
arr[:, c:c+1]       # column c kept as a 2D column (shape (rows, 1))
arr[r1:r2]          # some rows, all columns (same as arr[r1:r2, :])
arr[:, ::2]         # every other column
arr[::-1, :]        # rows in reverse order

Example — columns and groups of rows

import numpy as np

scores = np.array([
    [72, 45, 88, 31, 64,  0, 103, 52],   # row 0: Virat
    [56,  0, 74, 88, 32, 45,  61, 17],   # row 1: Rohit
    [45, 32,  0, 67, 18, 54,  78, 22],   # row 2: Hardik
])

print("Match 1, all players :", scores[:, 0])
print("Last match, all      :", scores[:, -1])
print("First two players:")
print(scores[:2])
print("Matches 3-5 of all players:")
print(scores[:, 2:5])

Match 1, all players : [72 56 45]
Last match, all      : [52 17 22]
First two players:
[[ 72  45  88  31  64   0 103  52]
 [ 56   0  74  88  32  45  61  17]]
Matches 3-5 of all players:
[[88 31 64]
 [74 88 32]
 [ 0 67 18]]

How it works: scores[:, 0] = every row, column 0 → one score per player. scores[:2] slices only axis 0, so all 8 columns come along. scores[:, 2:5] keeps all rows but only columns 2, 3, 4.

Example — sub-matrix and stepped slices

scores = np.array([
    [72, 45, 88, 31, 64,  0, 103, 52],   # row 0: Virat
    [56,  0, 74, 88, 32, 45,  61, 17],   # row 1: Rohit
    [45, 32,  0, 67, 18, 54,  78, 22],   # row 2: Hardik
])

print("Virat & Rohit, matches 1-4:")
print(scores[0:2, 0:4])
print("Every other match, all players:")
print(scores[:, ::2])
print("Players in reverse order, last 3 matches:")
print(scores[::-1, -3:])

Virat & Rohit, matches 1-4:
[[72 45 88 31]
 [56  0 74 88]]
Every other match, all players:
[[ 72  88  64 103]
 [ 56  74  32  61]
 [ 45   0  18  78]]
Players in reverse order, last 3 matches:
[[ 54  78  22]
 [ 45  61  17]
 [  0 103  52]]

How it works: 0:2 on rows and 0:4 on columns cut out a 2×4 block. ::2 on columns picks columns 0, 2, 4, 6. ::-1 on rows flips the player order.

Example — integer vs slice changes the shape

scores = np.array([
    [72, 45, 88, 31, 64,  0, 103, 52],   # row 0: Virat
    [56,  0, 74, 88, 32, 45,  61, 17],   # row 1: Rohit
    [45, 32,  0, 67, 18, 54,  78, 22],   # row 2: Hardik
])

print(scores[1, :].shape)     # integer on axis 0 -> row as 1D
print(scores[1:2, :].shape)   # slice on axis 0   -> stays 2D
print(scores[:, 0].shape)     # integer on axis 1 -> column as 1D
print(scores[:, 0:1].shape)   # slice on axis 1   -> column as 2D
print(scores[:, 0:1])

(8,)
(1, 8)
(3,)
(3, 1)
[[72]
 [56]
 [45]]

How it works: an integer index "uses up" its axis, so a column taken with [:, 0] is a flat 1D array of 3 values. A slice 0:1 keeps the axis with length 1, giving a 3×1 column vector — useful later for broadcasting.

Quick reference

Common mistakes

• ❌ scores[0:2][0:4] for a sub-matrix. ✅ That slices rows twice (rows 0–1, then rows 0–1 of those). Use scores[0:2, 0:4].
• ❌ Expecting scores[:, 0] to be a 3×1 column. ✅ It is 1D (3,); use scores[:, 0:1] (or scores[:, [0]]) to keep 2D.
• ❌ Forgetting stop is excluded on each axis: scores[0:1, 0:1] is a 1×1 array, not 2×2.
• ❌ Editing a slice "to try something" and being surprised that scores changed. ✅ Slices are views — call .copy() first.

Interview tip

Q: What is the difference between arr[:, 0] and arr[:, [0]]? A: arr[:, 0] uses an integer, so the column axis disappears → shape (rows,), a view. arr[:, [0]] uses a list (fancy indexing), so the axis stays → shape (rows, 1), and it is a copy.