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In Python, you can represent a two-dimensional structure as a list of lists, with each inner list holding one row. For numerical work, convert that structure to a NumPy ndarray to get explicit dimensions, convenient row-and-column indexing, and elementwise arithmetic.
Make a 2D structure with a nested list
A regular 2D structure has rows and columns. In a Python list of lists, each inner list is a row:
rows = [
[1, 2],
[3, 4],
[5, 6],
]
print(rows[0][1]) # 2
Python indexes from zero, so rows[0][1] selects the item in the first row and second column. For a rectangular grid, each inner list should have the same length. Lists can contain rows of different lengths, but such data is not a regular rectangle; check row lengths if your algorithm relies on a fixed number of columns. The Python tutorial’s list examples describe a matrix as a list of lists with equal-length rows.
Convert nested lists to a NumPy array
Install NumPy in your Python environment if it is not already available, then pass the nested sequence to np.array:
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import numpy as np
rows = [[1, 2], [3, 4], [5, 6]]
array = np.array(rows)
print(array)
print(array.shape) # (3, 2)
print(array.ndim) # 2
print(array.size) # 6
print(array.dtype) # inferred from the values
shape gives the length of each axis—in this case, three rows and two columns. ndim is the number of axes, size is the total number of elements, and dtype identifies the element type. NumPy infers a dtype from the input unless you specify one. If your code requires a particular numeric representation, set it explicitly:
floats = np.array([[1, 2], [3, 4]], dtype=np.float64)
Other constructors create arrays directly from a shape or a sequence of values:
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zeros = np.zeros((2, 3))
ones = np.ones((2, 3), dtype=int)
sequence = np.arange(6).reshape(2, 3)
For reshape, the number of values must fit the requested dimensions. See NumPy’s official guides to array creation and basic array concepts and operations.
Select rows, columns, and individual values
Built-in lists use chained indexing; NumPy arrays accept row and column indexes separated by a comma. Both forms use zero-based indexes.
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| What you want | List of lists | NumPy array |
|---|---|---|
| Item in first row, second column | rows[0][1] |
array[0, 1] |
| Second row | rows[1] |
array[1] |
| First column | [row[0] for row in rows] |
array[:, 0] |
| First two rows, columns from index 1 onward | [row[1:] for row in rows[0:2]] |
array[0:2, 1:] |
For example, with array = np.array([[10, 11, 12], [20, 21, 22]]), array[0, 1] is 11, array[1] is the second row, and array[:, 0] selects the first column. A built-in list does not use rows[0, 1] for this: that syntax supplies a tuple as one index, whereas a list expects a single index. NumPy’s indexing and slicing guide covers indexing along multiple axes.
Use NumPy for elementwise arithmetic
Adding a number to a NumPy array adds it to every element. Ordinary list operations do not provide the same elementwise numeric behavior; use a loop or another explicit calculation for lists.
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array = np.array([[1, 2], [3, 4]])
print(array + 10)
# [[11 12]
# [13 14]]
NumPy can also apply an operation between arrays with compatible shapes. For example, a one-dimensional array of length two is broadcast across the rows of a 2-by-2 array:
array = np.array([[1, 2], [3, 4]])
scaled = array * np.array([10, 100])
print(scaled)
# [[ 10 200]
# [ 30 400]]
The row-shaped operand supplies one multiplier per column. Broadcasting is not arbitrary alignment: dimensions must be compatible under NumPy’s rules. NumPy’s documentation defines broadcasting as how arrays with different shapes are treated during arithmetic and notes that it can avoid needless copies, though some broadcasting patterns can use memory inefficiently. Read the broadcasting guide when working with shapes beyond simple examples.
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Understand slicing, views, and copies
Basic NumPy slicing can produce a view that refers to the original array’s data. Changing the view can therefore change the original:
original = np.array([[1, 2], [3, 4]])
row_view = original[0]
row_view[0] = 99
print(original[0, 0]) # 99
Call .copy() when you need independent array data:
independent = original[0].copy()
independent[0] = -1
print(original[0, 0]) # still 99
Python list slicing behaves differently: it creates a new list containing references to the selected elements. It does not recursively copy mutable objects nested inside that list. NumPy explains the distinction between views and copies in its documentation.
Choose a list of lists or a NumPy array
| Use case | Better fit | Why |
|---|---|---|
| Flexible, general-purpose nested data or a small structure without numerical array operations | List of lists | Each row is an ordinary Python list that can be manipulated as a general-purpose object. |
| Regular numerical data, multidimensional indexing, or repeated elementwise calculations | NumPy ndarray |
It provides shape and dtype information, comma-separated axis indexing, and array arithmetic. |
There is no universal speed ratio that applies to every list and array workload. Performance depends on the operation, data, and environment, so use a benchmark suited to your actual task if speed is the deciding factor.
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