How to Learn Linear Algebra for Machine Learning? [Step-by-Step]

How to Learn Linear Algebra for Machine Learning?

Do you want to know How to Learn Linear Algebra for Machine Learning?… If yes, this blog is for you. In this blog, I will explain a step-by-step guide to Learn Linear Algebra for Machine Learning.

How to Learn Linear Algebra for Machine Learning?

1. Introduction

Linear algebra is a branch of mathematics that deals with linear equations, functions, and their representation through vectors and matrices. In the context of machine learning, linear algebra is like your toolkit for understanding and solving complex problems. In this guide, we will help you navigate this toolkit in a way that is friendly and approachable.

2. Why Learn Linear Algebra for Machine Learning?

Let’s begin with why it’s important to dive into linear algebra when entering the world of machine learning:

  • Data Magic: Machine learning often involves working with large datasets. Linear algebra helps make sense of this data by organizing it into neat matrices.
  • Dimension Whisperer: Linear algebra techniques, such as Principal Component Analysis (PCA), allow you to reduce data dimensions while preserving the essence of your data.
  • Solving Puzzles: Many machine learning problems boil down to solving systems of linear equations. Linear algebra techniques come to the rescue.
  • Machine Learning Magic: Popular machine learning models, like support vector machines and neural networks, rely heavily on linear algebra for training and predictions.
  • Understanding is Empowerment: Even if you use libraries and tools to implement machine learning algorithms, understanding the math behind them empowers you to optimize and troubleshoot effectively.

3. The Building Blocks of Linear Algebra

a. Scalars and Vectors

  • Scalar: A single number, like 5 or -2.7.
  • Vector: Think of it as a collection of numbers neatly lined up, for instance, [3, 1, 4].

b. Matrices

  • Matrix: It’s like a grid of numbers, arranged in rows and columns, for example,
   | 2  3 |
   | 1  0 |

c. Transposition

  • Transposition: Imagine flipping a matrix like a pancake; rows become columns, and columns become rows.

d. Matrix Multiplication

  • Matrix Multiplication: It’s a way of mixing two matrices to create a new one.
  • Dot Product: This is a particular type of matrix multiplication that has its own magic.

e. The Identity Matrix

  • Identity Matrix: It’s a special matrix with ones on the diagonal and zeros elsewhere.
  • Multiplication by Identity: When you multiply a matrix by the identity matrix, it stays the same.

f. Inverse Matrix

  • Inverse Matrix: A matrix that, when multiplied by another, gives the identity matrix.
  • Not All Matrices Are Invertible: Some matrices don’t have inverses.

4. Linear Transformations

a. Scaling and Translation

  • Scaling: Think of making something bigger or smaller.
  • Translation: It’s like shifting something’s position.

b. Rotation

  • Rotation: It’s as if you’re turning an object around a fixed point.
  • Rotational Matrices: These are like special codes for performing rotations.

c. Shearing

  • Shearing: Picture it as distorting an object by skewing it along a particular axis.

5. Vector Spaces: Where Vectors Roam

a. Basis and Dimension

  • Basis: This is like the “alphabet” for vectors. It’s a set of special vectors.
  • Dimension: It’s the number of vectors in the basis set.

b. Linear Independence

  • Linear Independence: A set of vectors is linearly independent if no vector in the set can be formed by combining the others.

c. Span

  • Span: Think of it as the “neighborhood” of vectors that you can reach by walking in different directions from a starting point.

6. Eigenvalues and Eigenvectors: Unearthing Key Players

What are Eigenvalues and Eigenvectors?

  • Eigenvalues: These are special numbers that tell you how much a matrix stretches or shrinks an eigenvector.
  • Eigenvectors: These are special vectors that only get scaled when you apply a matrix to them.

Their Applications in Machine Learning

  • Dimensionality Reduction: Eigenvalues and eigenvectors play a crucial role in techniques like Principal Component Analysis (PCA).
  • Kernel Methods: In algorithms like Support Vector Machines (SVM), they are essential in decision-making.

7. Solving Linear Systems: The Crux of Many Problems

a. Gaussian Elimination

  • Gaussian Elimination: It’s like a puzzle-solving method for systems of linear equations. You tweak the equations until you reach a simple solution.

b. Matrix Inversion Method

  • Matrix Inversion Method: This approach involves finding the inverse of the matrix of coefficients to solve linear systems.

c. Matrix Factorization (LU Decomposition)

  • LU Decomposition: It’s a way to break down a matrix into two simpler pieces, making it easier to solve linear systems.

8. Applications in Machine Learning

Principal Component Analysis (PCA)

  • PCA: This technique helps simplify complex data by reducing its dimension while preserving the most important information.

Support Vector Machines (SVM)

  • SVM: This machine learning algorithm relies on linear algebra to find the best way to separate different classes of data.

Neural Networks

  • Neural Networks: These deep learning models depend heavily on linear algebra for their operations, like making predictions and learning from data.

9. Learning Linear Algebra

Online Courses and Tutorials

Practical Exercises

  • Practice Problems: The more you practice, the better you get. Solving exercises and problems is key to understanding.
  • Online Platforms: Websites like LeetCode and HackerRank offer exercises related to linear algebra.

Study Groups

  • Join a Study Group: Collaborating with others helps you learn faster. Together, you can discuss and tackle problems.
  • Online Forums: Platforms like Stack Overflow and Reddit have communities where you can seek help and share knowledge.


Linear algebra might sound like a daunting topic, but it’s your trusty sidekick in the world of machine learning. By understanding these fundamental concepts, you’ll unlock the inner workings of algorithms, fine-tune your models, and contribute to the exciting field of artificial intelligence. Whether you’re just starting or have some prior knowledge, there are plenty of friendly resources available to help you master this essential mathematical foundation for machine learning. Embrace the math, and let it be your guiding light on your machine-learning adventure.

Happy learning!


Thank YOU!

Though of the Day…

Anyone who stops learning is old, whether at twenty or eighty. Anyone who keeps learning stays young.

– Henry Ford

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