Linear Algebra for Data Science & Machine Learning in Python

Name: Linear Algebra for Data Science & Machine Learning in Python
Rating: 4.2 (23 reviews)

Vectors, Matrices, Systems of Linear Equations, Factorization, Eigenvectors, Least Squares, SVD

Created bySyed Mohiuddin

Last updated 11/2025

English

What you'll learn

Fundamentals of Linear Algebra
Applications of Vectors and Matrices with implementation in Python
Operations on Vectors and Matrices with implementation in Python
Solve Systems of Linear Equations and implementation in Python
Matrix Factorization and implementation in Python
Computation of Eigenvalues, Eigenvectors
Singular Value Decomposition with its implementation in Python
Eigen Decomposition with their implementation in Python

Course content

19 sections • 150 lectures • 9h 51m total length

What you are going to learn in this course2:50
Introduction1:47
What is Linear Algebra?1:10
Why Linear Algebra?0:56

Scalars and Vectors7:41
Scalars and Vectors
Vectors in 2-Dimensional Space4:32
Vectors
Vectors in 3-Dimensional Space2:41
Vectors with n-Components3:20
Explore vectors in n dimensional space and represent data with rn column vectors. See how eight weather attributes form an eight-dimensional vector and relate to r2 and r3.
Python Code - Creating Vectors10:29
Creating Vectors
Python Code - Creating Vectors using arange()6:00
Creating Vectors as sequence of numbers
Python Code - Accessing and Modifying Vectors4:07
Access and modify vector elements in python using zero-based indexing with numpy. Use L[0] and L[3] to access, L[2] = 35 to modify, and note index errors for out-of-range access.
Accessing and Modifying Vectors
Zero and Ones Vectors2:04
Python Code - Zero and Ones Vector3:45
Zero and Ones Vectors
Quiz Solutions0:03

Vector Addition4:16
Add two column vectors by summing corresponding components to obtain a new vector. Ensure both vectors have the same dimension, with examples in R2, R3, and Rn.
Python Code - Vector Addition4:03
Vector Addition
Scalar Multiplication4:55
Python Code - Scalar Multiplication4:58
Scalar Multiplication
Vector Properties2:45
Vector Properties
Linear Combinations of Vectors2:05
Python Code - Linear Combinations of Vectors2:47
Linear Combination
Vector Transpose2:19
Python Code - Vector Transpose2:10
Vector Transpose
Dot Product or Inner Product5:56
Explore the dot product (inner product) of two vectors, computed as a transpose times the vector, yielding a scalar that signals similarity and direction in r2 and r3.
Python Code - Dot Product7:58
Dot Product
Outer Product7:18
Python Code - Outer Product5:56
Outer Product
Quiz Solutions0:03

Matrices - Context of Data Science4:10
Matrices
Dimension or Size4:23
Python Code - Creating Matrices using array()6:10
Python Code - Creating Matrices using mat()5:27
Matrices
Python Code - Accessing and Modifying Elements4:11
Matrix Transpose4:41
Python Code - Matrix Transpose3:00
Matrix Transpose
Symmetric Matrix4:25
Python Code - Symmetric Matrix6:25
Symmetric Matrix
Identity Matrices1:42
Python Code - Identity Matrices4:15
Identity Matrix
Diagonal Matrix2:00
Python Code - Diagonal Matrix2:54
Diagonal Matrix
Triangular Matrix1:37
Triangular Matrix
Zero and Ones Matrix2:04
Python Code - Zero and Ones Matrix2:46
Zero and Ones Matrix
Quiz Solutions0:03

Matrix Addition5:32
Perform matrix addition by adding corresponding elements of matrices with the same dimensions, applied element-wise to A and B (e.g., two by two or two by three).
Python Code - Matrix Addition3:47
Matrix Addition
Scalar Multiplication4:12
Python Code - Scalar Multiplication2:30
Learn how to perform scalar multiplication on matrices in python with numpy, applying a scalar to each matrix element and displaying the resulting matrix.
Scalar Multiplication
Hadamard Product5:38
Python Code - Hadamard Product4:08
Hadamard Product
Trace of Matrix2:39
Python Code - Trace of Matrix3:14
Matrix Trace
Matrix Multiplication5:21
Python Code - Matrix Multiplication4:35
Matrix Multiplication
Properties of Matrix Operations4:09
Matrix Power1:23
Python Code - Matrix Power4:17
Learn how to compute the matrix power using NumPy's linalg.matrix_power, with square matrices, and see practical examples that multiply a matrix by itself several times.
Matrix Power
Diagonal Matrix Multiplication6:04
Python Code - Diagonal Matrix Multiplication5:57
Quiz Solutions0:03

System of Linear Equations6:41
System of Linear Equations
Types of Systems3:20
Explore how systems of linear equations yield a unique solution, infinitely many solutions, or no solution by graphing lines and identifying intersection points, with examples demonstrating consistency and inconsistency.
Matrix Notation2:55
Matrix Notation
Elementary Row Operations6:40
Gauss Elimination Method9:40
Gaussian elimination with elementary row operations to transform an augmented matrix into row echelon form, then use back substitution to solve for x1, x2, and x3.
Gauss Elimination Method
Gauss-Jordan Elimination Method7:00
Learn the Gauss-Jordan elimination method to turn an augmented matrix into row reduced echelon form and solve a system of linear equations by row operations.
Python Code - Gauss Jordan Elimination Method8:22
Gauss-Jordan Elimination Method
Quiz Solutions0:03

Matrix Vector Product Ax=b5:25
Matrix Vector Product
Systems of Equations as Linear Combinations4:32
Classification of Matrix Vector Product4:21
Solving Systems of Linear Equations using Matrix Inverse5:23
Python Code - Solving Systems of Linear Equations using Matrix Inverse8:53
Solving Systems of Linear Equations using Matrix Inverse
Solving Systems of Linear Equations using Cramer's Rule4:21
Python Code - Solving Systems of Linear Equations using Cramer's Rule7:40
Solve a two-equation, two-unknown system using Cramer's rule. Represent the coefficients as matrix A and the constants as vector B to compute x1 and x2 via determinants.
Solving Systems of Linear Equations using Cramer's Rule
Python Code - Solving Systems of Linear Equations using solve()7:51
Quiz Solutions0:03

Requirements

You should have familiarity with fundamentals of Maths
All the implementation of Linear Algebra concepts are in Python, so familiarity with Python will be an added advantage

Description

This course will help you in understanding of the Linear Algebra and math’s behind Data Science and Machine Learning. Linear Algebra is the fundamental part of Data Science and Machine Learning. This course consists of lessons on each topic of Linear Algebra + the code or implementation of the Linear Algebra concepts or topics.

There’re tons of topics in this course. To begin the course:

We have a discussion on what is Linear Algebra and Why we need Linear Algebra
Then we move on to Getting Started with Python, where you will learn all about how to setup the Python environment, so that it’s easy for you to have a hands-on experience.

Then we get to the essence of this course;

Vectors & Operations on Vectors
Matrices & Operations on Matrices
Determinant and Inverse
Solving Systems of Linear Equations
Norms & Basis Vectors
Linear Independence
Matrix Factorization
Orthogonality
Eigenvalues and Eigenvectors
Singular Value Decomposition (SVD)

Again, in each of these sections you will find Python code demos and solved problems apart from the theoretical concepts of Linear Algebra.

You will also learn how to use the Python's numpy library which contains numerous functions for matrix computations and solving Linear Algebric problems.

So, let’s get started….

Who this course is for:

Anyone who is curious about how Linear Algebra is used in Machine Learning
Anyone who wants to understand Maths and Linear Algebra behind Data Science
Anyone who wants to develop fundamental foundations for deployment of Machine Learning Techniques

Linear Algebra for Data Science & Machine Learning in Python

What you'll learn

Explore related topics

Course content

Introduction4 lectures • 7min

Getting Started with Python2 lectures • 13min

Vectors10 lectures • 45min

Operations on Vectors14 lectures • 57min

Matrices17 lectures • 1hr

Operations on Matrices16 lectures • 1hr 3min

Matrix Determinant and Inverse9 lectures • 31min

System of Linear Equations8 lectures • 45min

Matrix Equations Ax=b9 lectures • 48min

Norms10 lectures • 28min

Requirements

Description

Who this course is for: