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.
课程信息
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第 3 门课程（共 4 门）
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中级
Some background in Python programming language and algebra.
完成时间大约为14 小时
英语（English）
字幕：英语（English）
可分享的证书
完成后获得证书
100% 在线
立即开始，按照自己的计划学习。
第 3 门课程（共 4 门）
可灵活调整截止日期
根据您的日程表重置截止日期。
中级
Some background in Python programming language and algebra.
完成时间大约为14 小时
英语（English）
字幕：英语（English）
提供方
国立高等经济大学
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.
教学大纲 - 您将从这门课程中学到什么
完成时间为 5 小时
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.
完成时间为 5 小时
15 个视频 （总计 118 分钟）, 2 个阅读材料, 2 个测验
15 个视频
Introduction to Linear Algebra42
Linear Algebra and Calculus4分钟
Matrices and Multidimensional Vectors10分钟
Matrix arithmetics6分钟
Properties of matrix operations and some special matrices10分钟
Vectors and matrices in Python4分钟
Systems of linear equations11分钟
Matrix inverse13分钟
Gaussian elimination. The first example4分钟
Elementary row operations6分钟
Gaussian elimination. Main theorem.5分钟
Gaussian Elimination. The algorithm.13分钟
The Inverse matrix with Gaussian elimination5分钟
LU and PLU decomposition17分钟
2 个阅读材料
About the University10分钟
Covered Python methods20分钟
1 个练习
Week 11小时
完成时间为 2 小时
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.
完成时间为 2 小时
14 个视频 （总计 86 分钟）
14 个视频
Abstract algebra and linear algebra11分钟
Axioms of vector spaces: first application6分钟
Examples of vector spaces8分钟
Subspaces1分钟
Linear combinations and spans2分钟
Basis and linear dependence7分钟
Dimension of a vector space5分钟
Examples of bases7分钟
Linear dependence and rank3分钟
Formula for the solution of a SLAE9分钟
An example of vector representation of the set of solutions7分钟
Rouché–Capelli Theorem4分钟
Full rank decomposition8分钟
1 个练习
Week 230分钟
完成时间为 2 小时
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.
完成时间为 2 小时
10 个视频 （总计 85 分钟）
10 个视频
Coordinates change example9分钟
Euclidean space8分钟
Geometry and Euclidean spaces1分钟
Orthogonal and orthonormal bases4分钟
Distance and orthogonal projections6分钟
Inconsistent systems and the least squares method12分钟
Linear regression example8分钟
Introduction to support vector machine16分钟
Linear regression and SVM with Python4分钟
1 个练习
Week 330分钟
完成时间为 4 小时
Final Project
In this week we will apply the acquired knowledge about linear regression and SVM models in this final project.
完成时间为 4 小时
1 个视频 （总计 2 分钟）, 1 个阅读材料, 2 个测验
1 个视频
1 个阅读材料
References and further reading10分钟
1 个练习
Life expectancy prediction quiz1小时
关于 Mathematics for Data Science 专项课程
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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