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⇱ Linear Algebra for Machine Learning and Data Science | Coursera

Linear Algebra for Machine Learning and Data Science

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Linear Algebra for Machine Learning and Data Science

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Gain insight into a topic and learn the fundamentals.
4.6

2,345 reviews

Intermediate level

Recommended experience

Flexible schedule
3 weeks at 10 hours a week
Learn at your own pace
95%
Most learners liked this course
Gain insight into a topic and learn the fundamentals.
4.6

2,345 reviews

Intermediate level

Recommended experience

Flexible schedule
3 weeks at 10 hours a week
Learn at your own pace
95%
Most learners liked this course

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

Build your subject-matter expertise

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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  • Gain a foundational understanding of a subject or tool
  • Develop job-relevant skills with hands-on projects
  • Earn a shareable career certificate

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 videos•Total 78 minutes
  • Specialization introduction•8 minutes
  • Course introduction•1 minute
  • What to expect and how to succeed•1 minute
  • A note on programming experience•1 minute
  • Linear Algebra Applied I•6 minutes
  • Linear Algebra Applied II•7 minutes
  • System of sentences•5 minutes
  • System of equations•13 minutes
  • System of equations as lines and planes•12 minutes
  • A geometric notion of singularity•3 minutes
  • Singular vs non-singular matrices•5 minutes
  • Linear dependence and independence•7 minutes
  • The determinant•8 minutes
  • Conclusion•0 minutes
8 readings•Total 72 minutes
  • Join the DeepLearning.AI Forum to ask questions, get support, or share amazing ideas!•2 minutes
  • Notations•10 minutes
  • Learning Python: Recommended Resources•10 minutes
  • Check your knowledge•10 minutes
  • Interactive Tool: Graphical Representation of Linear Systems with 2 variables•10 minutes
  • Interactive Tool: System of Equations as Planes (3x3)•10 minutes
  • (Optional) Downloading your Notebook and Refreshing your Workspace•10 minutes
  • Week 1 - Slides•10 minutes
3 assignments•Total 210 minutes
  • Practice Quiz 1•60 minutes
  • Practice Quiz 2•30 minutes
  • Graded quiz•120 minutes
1 app item•Total 1 minute
  • Intake Survey•1 minute
2 ungraded labs•Total 120 minutes
  • Introduction to NumPy Arrays•60 minutes
  • Linear Systems as Matrices•60 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 videos•Total 49 minutes
  • Solving non-singular system of linear equations•7 minutes
  • Solving singular system of linear equations•3 minutes
  • Solving system of equations with more variables•3 minutes
  • Matrix row-reduction•4 minutes
  • Row operations that preserve singularity•4 minutes
  • The rank of a matrix•6 minutes
  • The rank of a matrix in general•2 minutes
  • Row echelon form•3 minutes
  • Row echelon form in general•4 minutes
  • Reduced row echelon form•4 minutes
  • The Gaussian Elimination Algorithm•9 minutes
  • Conclusion•1 minute
5 readings•Total 45 minutes
  • Check your knowledge•10 minutes
  • Interactive Tool: Graphical Representation of Linear Systems with 3 variables•10 minutes
  • (Optional) Assignment Troubleshooting Tips•10 minutes
  • (Optional) Partial Grading for Assignments•10 minutes
  • Week 2 - Slides•5 minutes
2 assignments•Total 150 minutes
  • Practice Quiz•30 minutes
  • Graded Quiz•120 minutes
1 programming assignment•Total 240 minutes
  • Gaussian Elimination•240 minutes
1 ungraded lab•Total 30 minutes
  • Introduction to the Numpy.linalg sub-library•30 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 videos•Total 54 minutes
  • Machine Learning Motivation•8 minutes
  • Vectors and their properties•5 minutes
  • Vector operations•3 minutes
  • The dot product•4 minutes
  • Geometric Dot Product•3 minutes
  • Multiplying a matrix by a vector•3 minutes
  • Matrices as linear transformations•3 minutes
  • Linear transformations as matrices•2 minutes
  • Matrix multiplication•6 minutes
  • The identity matrix•1 minute
  • Matrix inverse•3 minutes
  • Which matrices have an inverse?•2 minutes
  • Neural networks and matrices•9 minutes
  • Conclusion•1 minute
3 readings•Total 25 minutes
  • Check your knowledge•10 minutes
  • Interactive Tool: Linear Transformations•10 minutes
  • Week 3 - Slides•5 minutes
2 assignments•Total 90 minutes
  • Practice Quiz•30 minutes
  • Graded Quiz•60 minutes
1 programming assignment•Total 240 minutes
  • Linear Transformations and Neural Networks•240 minutes
3 ungraded labs•Total 180 minutes
  • Vector Operations: Scalar Multiplication, Sum and Dot Product of Vectors•60 minutes
  • Matrix Multiplication•60 minutes
  • Linear Transformations•60 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 videos•Total 99 minutes
  • Week 4 Introduction•5 minutes
  • Singularity and rank of linear transformations•4 minutes
  • Determinant as an area•3 minutes
  • Determinant of a product•4 minutes
  • Determinants of inverses•3 minutes
  • Bases in Linear Algebra•3 minutes
  • Span in Linear Algebra•9 minutes
  • Eigenbases•3 minutes
  • Eigenvalues and Eigenvectors•6 minutes
  • Calculating Eigenvalues and Eigenvectors•9 minutes
  • On the Number of Eigenvectors•9 minutes
  • Dimensionality Reduction and Projection•8 minutes
  • Motivating PCA•3 minutes
  • Variance and Covariance•7 minutes
  • Covariance Matrix•8 minutes
  • PCA - Overview•5 minutes
  • PCA - Why It Works•4 minutes
  • PCA - Mathematical Formulation•2 minutes
  • Discrete Dynamical Systems•5 minutes
  • Conclusion•0 minutes
7 readings•Total 65 minutes
  • Check your knowledge•10 minutes
  • Interactive Tool: Linear Span•10 minutes
  • Week 4 - Slides•5 minutes
  • How is your course experience so far?•10 minutes
  • Reading: Textbooks and resources•10 minutes
  • References•10 minutes
  • Acknowledgments•10 minutes
2 assignments•Total 121 minutes
  • Practice Quiz•1 minute
  • Graded Quiz•120 minutes
1 programming assignment•Total 120 minutes
  • Application of Eigenvalues and Eigenvectors: Webpage navigation model and PCA•120 minutes
1 ungraded lab•Total 60 minutes
  • Interpreting Eigenvalues and Eigenvectors•60 minutes

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Instructor

Instructor ratings
4.7 (745 ratings)
DeepLearning.AI
4 Courses•250,760 learners

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Showing 3 of 2345

MS
·

Reviewed on Aug 26, 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.

RK
·

Reviewed on Sep 22, 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.

SP
·

Reviewed on Jul 26, 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.

Frequently asked questions

This is a beginner-friendly course, aiming to teach the concepts covered with minimal background knowledge necessary. If you're familiar with the concepts of linear algebra, you'll find this course a good review for the next course in the specialization, Calculus for Machine Learning and Data Science.

Yes! We want to break down the barriers that hold people back from advancing their math skills. In this course, we flip the traditional mathematics pedagogy for teaching math, starting with the real world use-cases and working back to theory.

Most people who are good at math simply have more practice doing math, and through that, more comfort with the mindset needed to be successful. This course is the perfect place to start or advance those fundamental skills, and build the mindset required to be good at math.

Linear algebra (matrices, vectors, and their applications)

With out-of-the-box tools, it’s easier than ever to begin a career as a machine learning engineer or data scientist. But to advance deeper in your career, create efficient models, troubleshoot algorithms, and incorporate creative thinking, a deeper understanding of the mathematics behind the models is needed.

No. Most learners would benefit from taking courses one and two together, as they introduce concepts that build upon each other, but course three is independent from the other courses in this specialization.

No, this Specialization is not for college credit.

Linear Algebra for Machine Learning and Data Science can be taken as a standalone course or the first course in the Mathematics for Machine Learning and Data Science Specialization.

Yes, Coursera provides financial aid to learners who cannot afford the fee.

To access the course materials, assignments and to earn a Certificate, you will need to purchase the Certificate experience when you enroll in a course. You can try a Free Trial instead, or apply for Financial Aid. The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.

When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile.

Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.

Financial aid available,