Math204
Linear Algebra 2
Faculty
Anier Velasco Sotomayor
Lead at the ML Theory group at Cohere for AI Open Science community.
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
This course prepares students for more advanced topics such as Machine Learning, Optimization Theory, Theory of Control and others.
Learning highlights
- Our main goal is to develop a good understanding of what linear transformations do.
- Based on this understanding, students will learn to analyze matrix properties such as determinants, eigenvalues and vectors, SVD decomposition and other matrix factorizations.
- Furthermore, students will learn some other topics such as tensors, Hilbert Spaces and Fourier Series.
Course outline
15 classes
Session 1
Rehearsal.
Linear transformations and the geometric meaning of them.
Session 2
Determinants. Properties of determinants.
Permutations and cofactors. Cramer’s rule, Inverse matrix. Determinant as volume.
Session 3
Eigenvectors and eigenvalues.
Equation for eigenvalues.
Power method.
Session 4
Symmetric matrices. Positive and negative definite matrices.
Matrix diagonalization.
Session 5
Seminar: Eigenvectors and eigenvalues.
Session 6
Covariance matrix. SVD. Diagonalization and pseudoinverses.
Session 7
Seminar: SVD.
Session 8
Linear transformation. Matrix of a linear transformation. Rotation matrix. Change of basis.
Session 9
Least squares solution. Matrix derivatives.
Session 10
Tensors and operations with tensors.
Einstein’s rule. Vectors and covectors. Differentiation with tensors.
Session 11
Complex vectors and matrices. Hermitian and Unary matrices.
Session 12
Hilbert spaces. Generalization of Scalar Product.
Fourier transform. Discrete Fourier transform.
Session 13
Inverse problems. Truncated SVD. Regularization.
Session 14
Seminar: Tensors.
Applications of linear algebra.
Session 15
Final exam.
Course materials
Books
Media
Prerequisites
Linear Algebra 1
Calculus (derivatives)
Python 1
Methodology
There will be theoretical and seminar sessions for solving problems, where there will be math and programming tasks.
Grading
Anier started in computer science by doing programming Olympiads in high school, during which he obtained a gold medal in the Cuban National Olympiad and a bronze medal in the Ibero-American Olympiad in Informatics.
He has a BSc. in Computer Science and Data Science from Harbour.Space University. His main professional interest is Machine Learning Theory Research, and he’s an independent researcher.
See full profileApply for this course
Linear Algebra 2
by Anier Velasco Sotomayor
Total hours
45 Hours
Dates
Nov 28 - Dec 16, 2022
Fee for single course
€1500
Fee for degree students
€750
How to secure your spot
Complete the form below to kickstart your application
Schedule your Harbour.Space interview
If successful, get ready to join us on campus
FAQ
Will I receive a certificate after completion?
Yes. Upon completion of the course, you will receive a certificate signed by the director of the program your course belonged to.
Do I need a visa?
This depends on your case. Please check with the Spanish or Thai consulate in your country of residence about visa requirements. We will do our part to provide you with the necessary documents, such as the Certificate of Enrollment.
Can I get a discount?
Yes. The easiest way to enroll in a course at a discounted price is to register for multiple courses. Registering for multiple courses will reduce the cost per individual course. Please ask the Admissions Office for more information about the other kinds of discounts we offer and what you can do to receive one.