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 part of the Mathematics for Data Science Specialization
Offered By
Mathematics for Data Science SpecializationNational Research University Higher School of EconomicsAbout this Course
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Intermediate Level
Some background in Python programming language and algebra.
Approx. 14 hours to complete
English
Subtitles: English
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Course 3 of 4 in the
Flexible deadlines
Reset deadlines in accordance to your schedule.
Intermediate Level
Some background in Python programming language and algebra.
Approx. 14 hours to complete
English
Subtitles: English
Offered by
National Research University Higher School of Economics
National Research University - Higher School of Economics (HSE) 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 National Research University Higher School of Economics.
If you are admitted to the full program, your courses count towards your degree learning.
Syllabus - What you will learn from this course
5 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.
5 hours to complete
15 videos (Total 118 min), 2 readings, 2 quizzes
15 videos
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
2 readings
About the University10m
Covered Python methods20m
1 practice exercise
Week 11h
2 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.
2 hours to complete
14 videos (Total 86 min)
14 videos
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
1 practice exercise
Week 230m
2 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.
2 hours to complete
10 videos (Total 85 min)
10 videos
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
1 practice exercise
Week 330m
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
1 video
1 reading
References and further reading10m
1 practice exercise
Life expectancy prediction quiz1h
About the Mathematics for Data Science Specialization
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.
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What will I get if I subscribe to this Specialization?
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Will I earn university credit for completing the Course?
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