2D Indexing: a[row, col]

Now the data is a table: 3 players (rows) × 8 matches (columns). To answer "What did Rohit score in match 3?" you need two positions — which row (player) and which column (match).

               match: 0    1    2    3    4    5    6    7
row 0  Virat     [   72,  45,  88,  31,  64,   0, 103,  52 ]
row 1  Rohit     [   56,   0,  74,  88,  32,  45,  61,  17 ]
row 2  Hardik    [   45,  32,   0,  67,  18,  54,  78,  22 ]
                  axis 1 (columns) ─────────────────────────►
axis 0 (rows) ▼

Definition

2D indexing selects an element of a 2D array by giving one index per axis, separated by a comma inside one pair of square brackets: arr[row, col]. The first index chooses the row (axis 0), the second chooses the column (axis 1).

• One index per axis — a 2D array has 2 axes, so a full address needs 2 numbers. Give both and you get a single scalar.
• Axis 0 = rows (here: players), axis 1 = columns (here: matches). scores.shape is (3, 8) → 3 rows, 8 columns.
• Fewer indexes than axes — arr[1] gives only the row index, so NumPy returns the whole row as a 1D array.
• Negative indexes work on every axis: arr[-1, -1] is the bottom-right cell.

Syntax

arr[r, c]      # single element at row r, column c  -> scalar
arr[r]         # whole row r                         -> 1D array (same as arr[r, :])
arr[-1, -1]    # last row, last column

Example — single cells

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("shape:", scores.shape)
print("Virat, match 1   :", scores[0, 0])
print("Rohit, match 3   :", scores[1, 2])
print("Hardik, last     :", scores[2, -1])
print("Bottom-right     :", scores[-1, -1])

shape: (3, 8)
Virat, match 1   : 72
Rohit, match 3   : 74
Hardik, last     : 22
Bottom-right     : 22

How it works: scores[1, 2] → row 1 (Rohit), column 2 (match 3) → 74. Each comma-separated number fixes one axis.

Example — a whole row with one index

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
])

rohit = scores[1]
print(rohit)
print("shape:", rohit.shape, " ndim:", rohit.ndim)
print("Rohit's total:", rohit.sum())

[56  0 74 88 32 45 61 17]
shape: (8,)  ndim: 1
Rohit's total: 373

How it works: with only the row index, NumPy fills the missing axis with "everything" (:). scores[1] is the same as scores[1, :]. An integer index removes that axis, so the 2D array becomes 1D with shape (8,).

a[row, col] vs a[row][col]

With a nested Python list you must write lst[1][2]. NumPy also accepts arr[1][2], and for a single element the answer is the same — but it works differently and it breaks with 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("scores[1, 2] =", scores[1, 2])
print("scores[1][2] =", scores[1][2])

# The difference appears with slices:
print("scores[:, 0] =", scores[:, 0])    # column 0 -> first match of every player
print("scores[:][0] =", scores[:][0])    # NOT column 0! -> row 0

scores[1, 2] = 74
scores[1][2] = 74
scores[:, 0] = [72 56 45]
scores[:][0] = [ 72  45  88  31  64   0 103  52]

How it works:

scores[:] is "all rows" — the whole array — and then [0] takes its first row. So arr[:][0] is not a column. Always use the comma form in NumPy.

Python list vs NumPy (2D)

Common mistakes

• ❌ scores[2, 8] for Hardik's 8th match. ✅ Columns are 0–7, so it's scores[2, 7] or scores[2, -1] — otherwise IndexError: index 8 is out of bounds for axis 1 with size 8.
• ❌ scores[:][0] to get the first column. ✅ scores[:, 0].
• ❌ Mixing up row and column order (scores[match, player]). ✅ Order follows the shape (3, 8) → [player, match].
• ❌ scores[1, 2, 0] on a 2D array. ✅ A 2D array accepts at most 2 indexes → IndexError: too many indices for array.

Interview tip

Q: Why prefer arr[i, j] over arr[i][j] in NumPy? A: arr[i, j] is a single indexing call with a tuple, so it is faster and works with slices on any axis (arr[:, j] is column j). arr[i][j] indexes twice; with slices it becomes (arr[:])[j], which selects a row, not a column.