Master Numpy: From Arrays to Matrix Operations in Python

1 Numpy

In Python we commonly use the Numpy library for array creation and function operations. It can be installed via the command line using:

<code>pip install numpy</code>

If you already use Anaconda, the library is pre‑installed and can be imported as np :

<code>import numpy as np</code>

2 Basic data type array

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

2.1 Creating array

Arrays can be created from a list:

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

Multi‑dimensional arrays can also be created:

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

2.2 Generating arithmetic sequences linspace and arange

Use linspace to generate a sequence with a specified number of elements:

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

Or use arange to specify step size:

<code>np.arange(1,10,2)  # [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</code>

Arrays can be reshaped, e.g., to 3 rows and 2 columns:

<code>a.reshape((3,2))</code>

2.4 Indexing data

<code>a[1,2]        # element in second row, third column
a[:,2]        # third column
a[:,[1,2]]   # second and third columns</code>

2.5 Filtering data

<code>a[a>2]                     # values greater than 2
a[(a>2)&(a<6)]            # values between 2 and 6</code>

3 Universal functions

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

<code>import math
import numpy as np
math.log(20)
np.log(20)
np.log([1,2,3])</code>

4 Matrix creation and operations

Numpy’s linalg module handles 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, inverse

<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</code>

4.3 Determinant, eigenvalues, eigenvectors

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