Course Descriptions
Matrix Analysis is an extension of the theory of linear equations and is one of the most important mathematical subjects that arise in the study, application and research of engineering and related sciences. The goal of this course is to introduce the foundations and main techniques of this theory at the graduate level, keeping a balance between classical and modern aspects. It is recommended that students who register at this class have had some prior experience with linear algebra, even though this is not strictly necessary.
Prerequisites
Compulsory: Linear Algebra, Mathematical Analysis or Advanced Calculus, Probability and Statistics.
Recommended Postrequisites: Mathematical and Numerical Optimization, Machine Learning.
Textbooks and Optional References
Textbook
Roger A. Horn and Charles R. Johnson, Matrix Analysis (Second Edition), Cambridge University Press, 2012.
Gene H. Golub and Charles F. Van Loan, Matrix Computations (Fourth edition), The John Hopkins University Press, 2013.
References
Carl D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM (Society for Industrial and Applied Mathematics), 2000.
Alan J. Laub, Matrix Analysis for Scientists & Engineers, SIAM (Society for Industrial and Applied Mathematics), 2004.
Steven Roman, Advanced Linear Algebra (Third Edition), Springer, 2007.
Schedule (Subject to Change)
Topic 0: Overview
Topic 1: Algebraic structure and linear transformations of abstract vector spaces
Topic 2: Matrices as coordinate representations of linear transformations
Topic 3: Elementary row/column operations, rank and fundamental spaces of matrices
Topic 4: Theory of determinants
Topic 5: Norms and orthogonal projections
Topic 6: QR decomposition, least-squares
Topic 7: Spectral theory (eigenvalues/eigenvectors)
Topic 8: Singular value decomposition
Topic 9: Variational and interlacing theorems for spectra of symmetric matrices
Topic 10: Robust and generalized principal component analysis
Topic 11: Module theory
Topic 12: Review
Note: Course materials are available on Piazza.com.
Assessment
100% weekly quiz.
Academic Integrity Policy
Group study and collaboration on problem sets are encouraged, as working together is a great way to understand new materials. Students are free to discuss the homework problems with anyone under the following conditions:
Students must write down their own solutions. Plagiarism is never allowed. Similar answers, MATLAB/Python/R codes, etc., found in HWs will invite you into suspected plagiarism investigation.
Students must list the names of their collaborators (i.e., anyone with whom the assignment was discussed).
Students can not use old solution sets from other classes under any circumstances, unless the instructor grants special permission.
Students are encouraged to read the ShanghaiTech Policy on Academic Integrity.
|