Linear Algebra for Data Science (2022)
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Содержание
General information
One semester course. 6 credits.
Lecturer: Dmitri Piontkovski (Дмитрий Игоревич Пионтковский)
Class teacher: Vsevolod Chernyshev (Всеволод Леонидович Чернышев)
Schedule
| Type | Day of week | Time | Place |
|---|---|---|---|
| Lectures | Friday | 18:10-19:30 | S224, Pokrovsky Blvd. 11 (Покровский б-р 11) |
| Seminars | Friday | 19:40-21:00 | S224, Pokrovsky Blvd. 11 (Покровский б-р 11) |
Grading system
Final Grade = 0.5 * Test1 + 0.5 * Test2 + Bonus (for a talk, ≤ 5) + Bonus (for classes, ≤1..2)
Tests: unique for everyone
Topics on which you can prepare a talk: on your own (based on your experience) or from list: will be published soon
Homeworks
| Type | Date | Topics | Download materials | Read Materials | Tasks | Time to completion | Deadline | Download Solution | Read Solution |
|---|---|---|---|---|---|---|---|---|---|
| Optional | 14.09.22 | Pseudoinverse matrices. Skeletonization. | Click | Click | 4 | 15-30 min | 16.09.22 | Click | Click |
| Soon | soon |
Lectures
All lectures you will find here
| Lecture | Date | Topics | Download materials | Read Materials | Pages | Reading time | GitHub (for changes) |
|---|---|---|---|---|---|---|---|
| Lecture 1 | 09.09.22 | Distinctive features of applied linear algebra. Problems with real data. Pseudoinverse matrices. Skeletonization. |
Click | Click | 3p | 7 min read | Click |
| Lecture 2 | 16.09.22 | Pseudosolutions and its applications. Linear Regression. | Click | Click | 3p (v1.0) | 10 min read | Click |
| Lecture 3 | 23.09.22 | Approximation. Interpolation problem. Polynomial interpolation. Hermitian interpolation. Splines. Bézier curves and splines. |
Click | Click | 5(v1.5) | 10 min read | Click |
| Lecture 4 | 07.10.22 | Metric axioms. Metric spaces. Norms. Normed linear spaces. | Click | Click | 4(v1.5) | 15 min read | Click |
| Lecture 5 | 14.10.22 | Norms. Minkovski's theorem. Euclidian space. | Click | Click | 1(v0) | 12 min read | Click |
| Lecture 6 | 21.10.22 | Chebyshev polynomials of the first kind. Chebyshev polynomials of the second kind. | Click | Click | 1(v0) | 12 min read | Click |
| Lecture 7 | soon | soon | soon | soon | soon | soon | soon |
Seminars
All seminars you will find here
| Seminar | Date | Topics | Download materials | Read Materials | Pages | Reading time | GitHub (for changes) |
|---|---|---|---|---|---|---|---|
| Seminar 1 | 09.09.22 | Pseudoinverse matrices. Skeletonization. Singular value decomposition (SVD) | Click | Click | 3p | 9 min read | GitHub link |
| Seminar 2 | 16.09.22 |
References
Main literature
- Тыртышников Е. Е. Матричный анализ и линейная алгебра. Учебное пособие. (2007)
- Беклемишев Д.В., Дополнительные главы линейной алгебры, СПБ, изд. Лань, 2008
- Шевцов Г.С. Линейная алгебра: теория и прикладные аспекты: Учеб. пособие. М.: Финансы и статистика, 2003 (или другой год издания). 576 с
- Olver, P.J., and Shakiban, C. Applied linear algebra. 2nd edition. Springer, 2018
- R. Horn and C. Jonson. Matrix analysis. 2nd edition. Cambridge Univ. Press, 2013
Additional literature
- Винберг Э.Б., Курс алгебры, М., изд. МГУ, 2002 (и последующие издания);
- Бахвалов Н., Жидков Н., Кобельков Н., Численные методы, М., изд. Бином, 2003 (или другой год издания);
- Колмогоров А.Н., Фомин С.В., Элементы теории функций и функционального анализа, М., изд. Наука, 1976 (или другой год издания);
- Aleskerov F., Ersel H., Piontkovski D. Linear Algebra for Economists. Berlin—Heidelberg, Springer, 2011;
- Bryan, K. and Leise, T., 2006. The $25,000,000,000 eigenvector: The linear algebra behind Google. SIAM review, 48(3), pp.569-581;
- D. Cox, J. Little, and D. O’Shea. Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra. Springer Science & Business Media, 2013.
