First Steps in Linear Algebra for Machine Learning

This course is part of the Mathematics for Data Science Specialization

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114 ratings

Dmitri Piontkovski +1 more instructor

21,875 already enrolled

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Part of the Master of Data Science degree

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Mathematics for Data Science SpecializationHSE University

About this Course

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The main goal of the course is to explain the main concepts of linear algebra that are used in data analysis and machine learning. Another goal is to improve the student’s practical skills of using linear algebra methods in machine learning and data analysis. You will learn the fundamentals of working with data in vector and matrix form, acquire skills for solving systems of linear algebraic equations and finding the basic matrix decompositions and general understanding of their applicability.
This course is suitable for you if you are not an absolute beginner in Matrix Analysis or Linear Algebra (for example, have studied it a long time ago, but now want to take the first steps in the direction of those aspects of Linear Algebra that are used in Machine Learning). Certainly, if you are highly motivated in study of Linear Algebra for Data Sciences this course could be suitable for you as well.

This Course is part of HSE University Master of Data Science degree program. Learn more about the admission into the program and how your Coursera work can be leveraged if accepted into the program here https://inlnk.ru/rj64e.

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Course 3 of 4 in the

Mathematics for Data Science Specialization

Intermediate Level

Some background in Python programming language and algebra.

Approx. 21 hours to complete

English

Subtitles: Arabic, French, Portuguese (European), Italian, Vietnamese, German, Russian, English, Spanish

Instructors

Instructor rating

4.27/5 (20 Ratings)

Dmitri Piontkovski

Professor

Faculty of Economic Sciences

22,110 Learners

2 Courses

Vsevolod L. Chernyshev

Associate Professor

Faculty of Computer Science

22,110 Learners

2 Courses

Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Course 3 of 4 in the

Mathematics for Data Science Specialization

Intermediate Level

Some background in Python programming language and algebra.

Approx. 21 hours to complete

English

Subtitles: Arabic, French, Portuguese (European), Italian, Vietnamese, German, Russian, English, Spanish

Offered by

HSE University

HSE University is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communicamathematics, engineering, and more.

Start working towards your Master's degree

This course is part of the 100% online Master of Data Science from HSE University. If you are admitted to the full program, your courses count towards your degree learning.

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Syllabus - What you will learn from this course

Content Rating88%(1,060 ratings)

Week

Week 1

9 hours to complete

Systems of linear equations and linear classifier

In the first week we provide an introduction to multi-dimensional geometry and matrix algebra. After that, we study methods for finding linear system solutions based on Gaussian eliminations and LU-decompositions. We illustrate the methods with Python code examples of matrix calculations.

9 hours to complete

15 videos (Total 118 min), 3 readings, 9 quizzes

15 videos

About the University1m

Introduction to Linear Algebra42s

Linear Algebra and Calculus4m

Matrices and Multidimensional Vectors10m

Matrix arithmetics6m

Properties of matrix operations and some special matrices10m

Vectors and matrices in Python4m

Systems of linear equations11m

Matrix inverse13m

Gaussian elimination. The first example4m

Elementary row operations6m

Gaussian elimination. Main theorem.5m

Gaussian Elimination. The algorithm.13m

The Inverse matrix with Gaussian elimination5m

LU and PLU decomposition17m

3 readings

About University10m

Rules on the academic integrity in the course10m

Covered Python methods20m

8 practice exercises

Matrices and multidimensional vectors15m

Matrix arithmetics30m

Systems of linear equations25m

Matrix inverse40m

Gaussian elimination. Main theorem20m

The Inverse matrix with Gaussian elimination20m

LU and PLU decomposition40m

Week 11h

Week

Week 2

4 hours to complete

Full rank decomposition and systems of linear equations

The second week is devoted to getting to know some fundamental notions of linear algebra, namely: vector spaces, linear independence, and basis. Next, we will discuss what a rank of a matrix is, and how it could help us decompose a matrix. In addition, we will talk about the properties of a set of solutions for a system of linear equations. At the end of this week we will apply this theory to a scanned document processing.

4 hours to complete

14 videos (Total 86 min)

14 videos

Overview of the second week1m

Abstract algebra and linear algebra11m

Axioms of vector spaces: first application6m

Examples of vector spaces8m

Subspaces1m

Linear combinations and spans2m

Basis and linear dependence7m

Dimension of a vector space5m

Examples of bases7m

Linear dependence and rank3m

Formula for the solution of a SLAE9m

An example of vector representation of the set of solutions7m

Rouché–Capelli Theorem4m

Full rank decomposition8m

5 practice exercises

Linear dependence and rank40m

An example of vector representation of the set of solutions25m

Rouché–Capelli Theorem25m

Full rank decomposition15m

Week 230m

Week

Week 3

4 hours to complete

Euclidean spaces

In the third week, we firstly introduce coordinates in an abstract vector space. This allows us to apply the usual matrix arithmetic to abstract vectors. Next, we discuss the concept of Euclidean space which allows us to measure distances and angles in vector spaces. Then we use these measures in the least squares method to find approximate solutions of linear systems and in the linear regression model based on it. Finally, we describe the core of the most common linear classifier called Support Vector Machine.

4 hours to complete

10 videos (Total 85 min)

10 videos

Coordinates and basis12m

Coordinates change example9m

Euclidean space8m

Geometry and Euclidean spaces1m

Orthogonal and orthonormal bases4m

Distance and orthogonal projections6m

Inconsistent systems and the least squares method12m

Linear regression example8m

Introduction to support vector machine16m

Linear regression and SVM with Python4m

6 practice exercises

Coordinates and basis20m

Coordinates change example30m

Euclidian space45m

Distance and orthogonal projections20m

Linear regression example15m

Week 330m

Week

Week 4

4 hours to complete

Final Project

In this week we will apply the acquired knowledge about linear regression and SVM models in this final project.

4 hours to complete

1 video (Total 2 min), 1 reading, 2 quizzes

Reviews

4.1

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2 stars
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1 star
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TOP REVIEWS FROM FIRST STEPS IN LINEAR ALGEBRA FOR MACHINE LEARNING

by AGJul 24, 2020

with great assignments,one could get relation of LA with computer science.For naive english it could hurdles at first.but nice content.must for intermediatory

by EADec 30, 2020

This is a well designed course, with the right balance of theory and practice. The quizzes and programming assignments reinforce the material effectively.

by KDAug 7, 2020

I learnt a lot with this course, good introduction to linear algebra, and good guidance to the use of sk-learn for Machine Learning.

by DCFeb 29, 2020

The material was very well presented, and the exercises were helpful for learning

View all reviews

About the Mathematics for Data Science Specialization

This Specialization is part of HSE University Master of Data Science degree program. Learn more about the admission into the program here and how your Coursera work can be leveraged if accepted into the program.

Behind numerous standard models and constructions in Data Science there is mathematics that makes things work. It is important to understand it to be successful in Data Science. In this specialisation we will cover wide range of mathematical tools and see how they arise in Data Science. We will cover such crucial fields as Discrete Mathematics, Calculus, Linear Algebra and Probability. To make your experience more practical we accompany mathematics with examples and problems arising in Data Science and show how to solve them in Python.

Frequently Asked Questions

When will I have access to the lectures and assignments?
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
The course may not offer an audit option. 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.
What will I get if I subscribe to this Specialization?
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. If you only want to read and view the course content, you can audit the course for free.
Is financial aid available?
Yes, Coursera provides financial aid to learners who cannot afford the fee. Apply for it by clicking on the Financial Aid link beneath the "Enroll" button on the left. You'll be prompted to complete an application and will be notified if you are approved. You'll need to complete this step for each course in the Specialization, including the Capstone Project. Learn more.

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First Steps in Linear Algebra for Machine Learning

About this Course