Arrays - what are they and multiple dimensions

What is a NumPy Array?

• A NumPy array (ndarray) is a grid of values (all of the same data type), stored in contiguous memory.
• Unlike Python lists, arrays are:
• Faster (implemented in C, vectorised operations).
• Memory efficient (fixed data type, compact storage).
• Support broadcasting and mathematical operations directly.

Think of it as a supercharged list designed for math and data manipulation.

Array Dimensions (Rank)

• The number of axes (dimensions) an array has is called its rank.
• NumPy arrays can be 1D, 2D, 3D, … nD.

1D Array (Vector)

A simple sequence of numbers (like a list):

import numpy as nparr1d = np.array([10, 20, 30, 40])print(arr1d.shape)  # (4,)

Looks like: [10, 20, 30, 40]

2D Array (Matrix)

Rows and columns:

arr2d = np.array([[1, 2, 3],                  [4, 5, 6]])print(arr2d.shape)  # (2, 3)

Looks like:

[[1 2 3] [4 5 6]]

3D Array (Tensor / Cube)

A stack of 2D arrays:

arr3d = np.array([[[1, 2], [3, 4]],                  [[5, 6], [7, 8]]])print(arr3d.shape)  # (2, 2, 2)

Think of it as 2 layers, each with 2 rows and 2 columns.

Higher Dimensions

• NumPy supports n-dimensional arrays (ndarray).
• Example: a 4D array could represent multiple 3D datasets (useful in deep learning, images, video frames, etc.).

Key Attributes of Arrays

Every NumPy array has:

• .ndim → number of dimensions.
• .shape → size along each dimension (tuple).
• .size → total number of elements.
• .dtype → data type of elements.

print(arr2d.ndim)   # 2 (2D array)​print(arr2d.shape)  # (2, 3) → 2 rows, 3 columns​print(arr2d.size)   # 6 (total elements)​print(arr2d.dtype)  # int64 (depends on system)

Why Multi-Dimensional Arrays?

• 1D → simple sequences (signals, series, vectors).
• 2D → tables, matrices (spreadsheets, images).
• 3D → stacked data (colour images with RGB channels, cubes).
• nD → higher-order data (video, deep learning tensors).