Master Numpy: Create Arrays, Perform Operations, and Harness Linear Algebra

1 Numpy

In Python we commonly use the Numpy library for array creation and function operations. It can be installed via the command line (cmd on Windows or Terminal on macOS) with:

<code>pip install numpy</code>

If you are using Anaconda, the library is already installed. The library is usually imported as np :

<code>import numpy as np</code>

2 Basic data type array

Numpy's basic data type is array , similar to Python's list but more powerful.

2.1 Generating array

Arrays can be created from a list:

<code>np.array([1,2,3])
# output: array(1,2,3)</code>

Multi‑dimensional arrays can also be generated:

<code>np.array([[1,2,3],[4,5,6]])  # 2 rows, 3 columns
# output: array([[1, 2, 3],
#                [4, 5, 6]])</code>

2.2 Generating arithmetic sequences linspace and arange

Use linspace to create an evenly spaced sequence by specifying the number of elements:

<code>np.linspace(1,10,5)
# output: array([ 1. ,  3.25,  5.5 ,  7.75, 10. ])</code>

Or use arange to specify the step size:

<code>np.arange(1,10,2)
# output: array([1, 3, 5, 7, 9])</code>

2.3 Shape and size

<code>a = np.array([[1,2,3],[4,5,6]])
a.shape   # (2, 3)
a.size    # 6
a.reshape((3,2))
# output: array([[1,2],
#                [3,4],
#                [5,6]])</code>

2.4 Indexing data

<code>a = np.array([[1,2,3],[4,5,6]])
a[1,2]      # 6
a[:,2]      # array([3,6])
a[:,[1,2]]  # array([[2,3],
#                [5,6]])</code>

2.5 Filtering data

<code>a = np.array([[1,2,3],[4,5,6]])
a[a>2]                     # array([3,4,5,6])
a[(a>2) & (a<6)]           # array([3,4,5])</code>

3 Universal functions

Numpy's universal functions ( ufuncs ) operate on entire arrays, unlike Python's math module which works on scalars. Example:

<code>import math, numpy as np
math.log(20)          # 2.995732...
np.log(20)            # 2.995732...
np.log([1,2,3])       # array([0., 0.69314718, 1.09861229])</code>

4 Matrix generation and operations

Numpy provides the linalg module for matrix calculations.

4.1 Common matrix generation

<code>np.eye(3)          # identity matrix
np.diag([1,2,3,4]) # diagonal matrix
np.zeros((3,4))    # 3×4 zero matrix</code>

4.2 Matrix addition, subtraction, multiplication, inversion

<code>A = np.array([[1,3,2],[4,1,5],[3,3,1]])
B = np.array([[3,3,1],[5,2,6],[1,2,3]])
A + B   # addition
A - B   # subtraction
A @ B   # matrix multiplication
np.linalg.inv(A)   # inverse of A</code>

4.3 Determinant, eigenvalues, eigenvectors

<code>np.linalg.det(A)               # determinant
values, vectors = np.linalg.eig(A)  # eigenvalues and eigenvectors</code>