Linear Algebra for Machine Learning and Data Science

Linear Algebra for Machine Learning and Data Science

This course is part of Mathematics for Machine Learning and Data Science Specialization

Instructor: Luis Serrano

What you'll learn

Represent data as vectors and matrices and identify their properties using concepts of singularity, rank, and linear independence
Apply common vector and matrix algebra operations like dot product, inverse, and determinants
Express certain types of matrix operations as linear transformation, and apply concepts of eigenvalues and eigenvectors to machine learning problems

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Assessments

9 assignments

Taught in English

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This course is part of the Mathematics for Machine Learning and Data Science Specialization

When you enroll in this course, you'll also be enrolled in this Specialization.

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There are 4 modules in this course

Newly updated for 2024! Mathematics for Machine Learning and Data Science is a foundational online program created by DeepLearning.AI and taught by Luis Serrano. In machine learning, you apply math concepts through programming. And so, in this specialization, you’ll apply the math concepts you learn using Python programming in hands-on lab exercises. As a learner in this program, you'll need basic to intermediate Python programming skills to be successful.

After completing this course, you will be able to: • Represent data as vectors and matrices and identify their properties using concepts of singularity, rank, and linear independence, etc. • Apply common vector and matrix algebra operations like dot product, inverse, and determinants • Express certain types of matrix operations as linear transformations • Apply concepts of eigenvalues and eigenvectors to machine learning problems Many machine learning engineers and data scientists need help with mathematics, and even experienced practitioners can feel held back by a lack of math skills. This Specialization uses innovative pedagogy in mathematics to help you learn quickly and intuitively, with courses that use easy-to-follow visualizations to help you see how the math behind machine learning actually works. We recommend you have a high school level of mathematics (functions, basic algebra) and familiarity with programming (data structures, loops, functions, conditional statements, debugging). Assignments and labs are written in Python but the course introduces all the machine learning libraries you’ll use.

Matrices are commonly used in machine learning and data science to represent data and its transformations. In this week, you will learn how matrices naturally arise from systems of equations and how certain matrix properties can be thought in terms of operations on system of equations.

What's included

14 videos8 readings3 assignments1 app item2 ungraded labs

14 videosTotal 78 minutes

Specialization introduction7 minutesPreview module
Course introduction1 minute
What to expect and how to succeed1 minute
A note on programming experience1 minute
Linear Algebra Applied I6 minutes
Linear Algebra Applied II6 minutes
System of sentences5 minutes
System of equations12 minutes
System of equations as lines and planes12 minutes
A geometric notion of singularity3 minutes
Singular vs non-singular matrices4 minutes
Linear dependence and independence7 minutes
The determinant7 minutes
Conclusion0 minutes

8 readingsTotal 72 minutes

[IMPORTANT] Have questions, issues or ideas? Join our Forum!2 minutes
Notations10 minutes
Learning Python: Recommended Resources10 minutes
Check your knowledge10 minutes
Interactive Tool: Graphical Representation of Linear Systems with 2 variables10 minutes
Interactive Tool: System of Equations as Planes (3x3)10 minutes
(Optional) Downloading your Notebook and Refreshing your Workspace10 minutes
Week 1 - Slides10 minutes

3 assignmentsTotal 210 minutes

Graded quiz120 minutes
Practice Quiz 160 minutes
Practice Quiz 230 minutes

1 app itemTotal 1 minute

Intake Survey1 minute

2 ungraded labsTotal 120 minutes

Introduction to NumPy Arrays60 minutes
Linear Systems as Matrices60 minutes

In this week, you will learn how to solve a system of linear equations using the elimination method and the row echelon form. You will also learn about an important property of a matrix: the rank. The concept of the rank of a matrix is useful in computer vision for compressing images.

What's included

12 videos5 readings2 assignments1 programming assignment1 ungraded lab

12 videosTotal 49 minutes

Solving non-singular system of linear equations6 minutesPreview module
Solving singular system of linear equations3 minutes
Solving system of equations with more variables2 minutes
Matrix row-reduction3 minutes
Row operations that preserve singularity3 minutes
The rank of a matrix5 minutes
The rank of a matrix in general2 minutes
Row echelon form3 minutes
Row echelon form in general4 minutes
Reduced row echelon form3 minutes
The Gaussian Elimination Algorithm8 minutes
Conclusion1 minute

5 readingsTotal 45 minutes

Check your knowledge10 minutes
Interactive Tool: Graphical Representation of Linear Systems with 3 variables10 minutes
(Optional) Assignment Troubleshooting Tips10 minutes
(Optional) Partial Grading for Assignments10 minutes
Week 2 - Slides5 minutes

2 assignmentsTotal 150 minutes

Graded Quiz120 minutes
Practice Quiz30 minutes

1 programming assignmentTotal 240 minutes

Gaussian Elimination240 minutes

1 ungraded labTotal 30 minutes

Introduction to the Numpy.linalg sub-library30 minutes

An individual instance (observation) of data is typically represented as a vector in machine learning. In this week, you will learn about properties and operations of vectors. You will also learn about linear transformations, matrix inverse, and one of the most important operations on matrices: the matrix multiplication. You will see how matrix multiplication naturally arises from composition of linear transformations. Finally, you will learn how to apply some of the properties of matrices and vectors that you have learned so far to neural networks.

What's included

14 videos3 readings2 assignments1 programming assignment3 ungraded labs

14 videosTotal 53 minutes

Machine Learning Motivation7 minutesPreview module
Vectors and their properties4 minutes
Vector operations3 minutes
The dot product4 minutes
Geometric Dot Product3 minutes
Multiplying a matrix by a vector3 minutes
Matrices as linear transformations2 minutes
Linear transformations as matrices1 minute
Matrix multiplication6 minutes
The identity matrix1 minute
Matrix inverse3 minutes
Which matrices have an inverse?1 minute
Neural networks and matrices9 minutes
Conclusion0 minutes

3 readingsTotal 25 minutes

Check your knowledge10 minutes
Interactive Tool: Linear Transformations10 minutes
Week 3 - Slides5 minutes

2 assignmentsTotal 90 minutes

Graded Quiz60 minutes
Practice Quiz30 minutes

1 programming assignmentTotal 240 minutes

Linear Transformations and Neural Networks240 minutes

3 ungraded labsTotal 180 minutes

Vector Operations: Scalar Multiplication, Sum and Dot Product of Vectors60 minutes
Matrix Multiplication60 minutes
Linear Transformations60 minutes

In this final week, you will take a deeper look at determinants. You will learn how determinants can be geometrically interpreted as an area and how to calculate determinant of product and inverse of matrices. We conclude this course with eigenvalues and eigenvectors. Eigenvectors are used in dimensionality reduction in machine learning. You will see how eigenvectors naturally follow from the concept of eigenbases.

What's included

20 videos7 readings2 assignments1 programming assignment1 ungraded lab

20 videosTotal 98 minutes

Week 4 Introduction4 minutesPreview module
Singularity and rank of linear transformations3 minutes
Determinant as an area3 minutes
Determinant of a product3 minutes
Determinants of inverses2 minutes
Bases in Linear Algebra2 minutes
Span in Linear Algebra8 minutes
Eigenbases3 minutes
Eigenvalues and Eigenvectors6 minutes
Calculating Eigenvalues and Eigenvectors8 minutes
On the Number of Eigenvectors8 minutes
Dimensionality Reduction and Projection7 minutes
Motivating PCA2 minutes
Variance and Covariance7 minutes
Covariance Matrix7 minutes
PCA - Overview4 minutes
PCA - Why It Works4 minutes
PCA - Mathematical Formulation2 minutes
Discrete Dynamical Systems5 minutes
Conclusion0 minutes

7 readingsTotal 65 minutes

Check your knowledge10 minutes
Interactive Tool: Linear Span10 minutes
Week 4 - Slides5 minutes
How is your course experience so far?10 minutes
Reading: Textbooks and resources10 minutes
References10 minutes
Acknowledgments10 minutes

2 assignmentsTotal 121 minutes

Graded Quiz120 minutes
Practice Quiz1 minute

1 programming assignmentTotal 120 minutes

Application of Eigenvalues and Eigenvectors: Webpage navigation model and PCA120 minutes

1 ungraded labTotal 60 minutes

Interpreting Eigenvalues and Eigenvectors60 minutes

Instructor

Instructor ratings

4.7 (631 ratings)

Luis Serrano

DeepLearning.AI

4 Courses176,042 learners

Offered by

DeepLearning.AI

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Reviewed on Aug 27, 2024

While people focus on teaching how to solve problems basically, It is very good to see people speak about maths like science as a concept with good visualization!. Great work guys.

Reviewed on Sep 23, 2023

I enjoyed the course very much but I found that week 4, especially the Eigenvalues and Eigenvectors explanation were not complete. This section can be definitely improved.

Reviewed on Jul 27, 2023

This course is truly exceptional for individuals eager to strengthen their grasp of Linear Algebra concepts, paving the way for a deeper understanding of machine learning and data science.

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