What is a Dimension (Axis)?

• A dimension (or axis) represents a direction along which you can access elements in an array.
• For a 1-dimensional array, there's only one axis.
• For a 2-dimensional array, there are two axes (rows and columns).
• For a 3-dimensional array, there are three axes (e.g., depth, rows, columns).

ndim Attribute

Every NumPy array has an ndim attribute, which returns the number of dimensions (axes) of the array.

shape Attribute

The shape attribute returns a tuple of integers indicating the size of the array along each dimension.

The length of the shape tuple is equal to ndim.

Dimensions

0-D Array (Scalar)

A 0-dimensional array, also known as a scalar, is a single element. It has no axes.

import numpy as np
arr = np.array(42)
print(arr)
print("Dimension:", arr.ndim)

#Output - 
42  
Dimension: 0

Key Points :

• It’s the simplest form of a NumPy array.
• Used when a single value is returned as an array object.
• .ndim returns 0, meaning zero dimensions.

Real-World Analogy :

Think of a 0-D array like a single coin — it’s not a row or table, just one item.

1-D Array (Vector)

A 1-D array (one-dimensional array) is like a simple list of values — a row of elements stored in a single line.

It has one axis.

import numpy as np

arr = np.array([10, 20, 30, 40, 50])
print(arr)
print("Dimension:", arr.ndim)

#Output - 
[10 20 30 40 50]  
Dimension: 1

Key Points :

• It's like a list or a row of elements.
• Has only one axis (axis 0).
• Very useful for simple data like marks, ages, etc.

Real-World Analogy :

A 1-D array is like a single row in Excel — just values from left to right.

2-D Array (Matrix)

A 2-D array is like a table — it has rows and columns. It’s the most commonly used array type in data science and machine learning.

import numpy as np
arr = np.array([[1, 2, 3], [4, 5, 6]])
print(arr)
print("Dimension:", arr.ndim)

#Output - 
[[1 2 3]
 [4 5 6]]
Dimension: 2

Key Points :

• 2 axes: rows (axis 0) and columns (axis 1).
• Shape here is (2, 3) → 2 rows, 3 columns.
• Ideal for representing matrices, spreadsheets, and images (in grayscale).

Real-World Analogy :

Think of a 2-D array like an Excel sheet with rows and columns filled with numbers.

3-D Array (Tensor)

A 3-D array is like a collection of 2-D arrays — imagine a cube or a stack of tables, one on top of the other.

import numpy as np

arr = np.array([
    [[1, 2, 3], [4, 5, 6]],
    [[7, 8, 9], [10, 11, 12]]
])
print(arr)
print("Dimension:", arr.ndim)

#Output - 
[[[ 1  2  3]
  [ 4  5  6]]

 [[ 7  8  9]
  [10 11 12]]]
Dimension: 3

Key Points :

1. It has 3 axes :

1. Axis 0: depth (2 blocks here)
2. Axis 1: rows
3. Axis 2: columns

2. Shape = (2, 2, 3) → 2 blocks, each with 2 rows and 3 columns.

Useful for representing :

• Colored images (RGB)
• Video frames
• Scientific data

Real-World Analogy :

Imagine a book with 2 pages, and each page has a table (2 rows × 3 columns).

n-D Array (n-Dimensional Array)

An n-D array is a general term for arrays with any number of dimensions (1D, 2D, 3D, 4D, ...).

In NumPy, you can create arrays with n dimensions, making it powerful for complex data like images, videos, simulations, and deep learning.

Example : Creating an n-D Array (4D)

import numpy as np
# 4-D array: shape (2, 2, 2, 3)
arr = np.array([[[[1, 2, 3], [4, 5, 6]],
                 [[7, 8, 9], [10, 11, 12]]],

                [[[13, 14, 15], [16, 17, 18]],
                 [[19, 20, 21], [22, 23, 24]]]])

print("Array:")
print(arr)
print("\nDimensions:", arr.ndim)
print("Shape:", arr.shape)

#Output - 
Array:
[[[[ 1  2  3]
   [ 4  5  6]]

  [[ 7  8  9]
   [10 11 12]]]


 [[[13 14 15]
   [16 17 18]]

  [[19 20 21]
   [22 23 24]]]]

Dimensions: 4
Shape: (2, 2, 2, 3)

Key Points :

1. ndim : Returns number of dimensions

2. shape : Tuple of size in each dimension

Real-Life Use Cases of n-D Arrays :

1D vs 2D vs 3D NumPy Arrays :

Summary

1. Use 1D for simple sequences.

2. Use 2D for tabular or matrix data.

3. Use 3D for stacking matrices (like images, RGB, etc.).