Working With 2D Arrays / Matrices

Whenever data has two dimensions — spreadsheets, images, game boards, matrices — a 2D array is the natural representation. Python supports two-dimensional structures via nested lists and, more powerfully, via the NumPy library. This chapter shows you both approaches with practical, real-world examples.

• Nested list: matrix = [[1,2,3], [4,5,6], [7,8,9]].
• Access an element with two indices: matrix[row][col].
• Use NumPy: np.array(...) or np.zeros((rows, cols)) for true matrices.
• Iterate row-by-row with nested loops, or use comprehensions for compact code.

# Pure Python
grid = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9],
]
print(grid[1][2])         # 6

# NumPy
import numpy as np
mat = np.array(grid)
print(mat.shape)          # (3, 3)
print(mat.T)              # transpose

• Definition: A 2D array organises data in rows and columns. Indexing requires two coordinates: row first, then column.
• Nested lists: Pure Python uses lists of lists. Flexible but slower and less feature-rich than NumPy.
• Initialising matrices: Use comprehensions for safety: [[0]*cols for _ in range(rows)]. Avoid [[0]*c]*r — it creates aliased rows!
• Traversal: Nested loops over rows and columns: for i in range(rows): for j in range(cols): .... Or unpacked: for row in matrix: for val in row: ....
• NumPy 2D arrays: np.array creates a real 2D array. Supports element-wise math, matrix multiplication (@), reshaping, and broadcasting.
• Common operations: Transpose: mat.T. Sum across rows/columns: mat.sum(axis=0). Matrix multiplication: a @ b.

mat = [[1,2,3], [4,5,6], [7,8,9]]
print("center:", mat[1][1])
for row in mat:
    print(row)

rows, cols = 3, 4
grid = [[0]*cols for _ in range(rows)]
grid[1][2] = 9
for r in grid:
    print(r)

mat = [[1,2,3], [4,5,6], [7,8,9]]
total = sum(v for row in mat for v in row)
print("Sum:", total)

mat = [[1,2,3], [4,5,6]]
trans = [list(r) for r in zip(*mat)]
print(trans)

import numpy as np
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
print(A @ B)

import numpy as np
m = np.array([[1,2,3], [4,5,6], [7,8,9]])
print("rows :", m.sum(axis=1))
print("cols :", m.sum(axis=0))

• Always initialise matrices with comprehensions, never [[0]*c]*r.
• Use NumPy when speed or math operations matter.
• Use zip(*matrix) for an elegant transpose of nested lists.
• Remember: matrix[row][col] — row first.
• For sparse matrices (mostly zeros), use scipy.sparse instead.
• Image libraries (PIL, OpenCV) all use NumPy 2D/3D arrays internally.

• Aliased rows: [[0]*c]*r creates the same row r times.
• Row/col mix-up: writing matrix[col][row] by mistake.
• Ragged 2D lists: nested lists may have uneven lengths — validate first.
• Treating Python list as matrix in math: use NumPy for matrix multiplication.
• Forgetting axis argument: arr.sum() reduces everything; pass axis=0/1.
• Indexing out of bounds: always check row and column counts before access.

• Problem 1: Print a 3×3 multiplication grid using nested for-loops.
• Problem 2: Read a 2D matrix from the user and print its transpose.
• Problem 3: Find the row with the maximum sum in a given matrix.
• Problem 4: Check whether a matrix is a square matrix and symmetric.
• Problem 5: Implement matrix addition without using NumPy.
• Problem 6: Use NumPy to compute the determinant and inverse of a 3×3 matrix.

• Q1. What is a 2D array and how is it represented in Python?
• Q2. Why is [[0]*c]*r dangerous?
• Q3. How do you transpose a 2D list without NumPy?
• Q4. What is matrix multiplication in NumPy and what operator does it use?
• Q5. How do you sum elements along a row vs along a column in NumPy?
• Q6. What is the difference between row-major and column-major order?

• Q1: How do I create a 2D array in Python?
  Use a list comprehension: [[0]*cols for _ in range(rows)] for pure Python, or np.zeros((rows, cols)) with NumPy.
• Q2: How do I iterate over a 2D array?
  Two nested for-loops: for i in range(rows): for j in range(cols): grid[i][j]. Or for row in grid: for v in row: ...
• Q3: How do I transpose a 2D list?
  List comprehension: [list(r) for r in zip(*matrix)]. With NumPy: arr.T.
• Q4: Why use NumPy 2D arrays over nested lists?
  Memory layout is contiguous, math operations are vectorised, and many libraries expect ndarrays.
• Q5: Can rows have different lengths?
  In nested lists, yes — but the result is ragged. NumPy arrays must be rectangular.
• Q6: How do I find a value's position in a matrix?
  Loop with index pairs, or with NumPy use np.where(arr == target).