🔵 Data Science · Lesson 44

Linear Algebra Basics

What are Linear Algebra Basics?

Linear Algebra Basics means linear algebra uses vectors and matrices. It is the mathematical base of many machine learning algorithms.

In real programs, this topic helps in vectors and matrices in ML. Learn the idea first, then type the program yourself and compare the output.

💡 At a Glance

Point	Details
Course Area	Data Science Tools and concepts used to analyse, clean and present data.
Main Use	vectors and matrices in ML
Example File	`linear-algebra-basics.py`
Practice Focus	Run, change values, and explain the output line by line.

Why should you learn this?

It is useful for vectors and matrices in ML.
It connects with feature representation.
It improves your ability to read, write and debug Python programs.

Important Terms

These terms are used directly in this lesson. Understand them before memorising the code.

Term	Meaning
vector	One-dimensional list of numbers used in maths and ML.
matrix	Two-dimensional arrangement of numbers.
dot product	Operation that multiplies and sums corresponding vector values.
shape	Dimensions of an array.
matrix multiplication	matrix multiplication is an important term in this topic.

Syntax / Basic Pattern

The simple pattern is: prepare data, apply the concept, then show the result.

Basic Pattern

import numpy as np
a = np.array([1, 2, 3])
b = np.array([4, 5, 6])
print("Dot product:", np.dot(a, b))
print("Vector addition:", a + b)

Complete Example Program

Python – linear-algebra-basics.py

import numpy as np

a = np.array([1, 2, 3])
b = np.array([4, 5, 6])

print("Dot product:", np.dot(a, b))
print("Vector addition:", a + b)

Expected Output

Dot product: 32 Vector addition: [5 7 9]

Program Explanation

import numpy as np imports ready-made features from a module/library.
a = np.array([1, 2, 3]) stores a value in a.
b = np.array([4, 5, 6]) stores a value in b.
print("Dot product:", np.dot(a, b)) displays information or calculated result on the screen.
print("Vector addition:", a + b) displays information or calculated result on the screen.

Where will you use it?

Vectors and matrices in ml.
Feature representation.
Model calculations.

Common Mistakes

Analysing data before checking missing values, duplicates and data types.
Changing original data without keeping a clean copy.
Creating charts without title, labels or explanation.

Practice Tasks

Type the program in linear-algebra-basics.py and run it.
Change input values or sample data and observe the new output.
Create one example related to vectors and matrices in ML.
Write 5 lines explaining the logic in your own words.

Summary

Linear Algebra Basics is not a theory-only topic. You should be able to explain the meaning, write the example, run it successfully, and use it in a small practical program.