Linear Algebra - acsl آزمایشگاه سیستم کنترل پیشرفته
Instructor
M. J. Yazdanpanah
Professor of Electrical Engineering
School of Electrical and Computer Eng., University of Tehran, Tehran, Iran
Office: Room #730, 7th floor, ECE Bldg.
Tel: 82084925
Email: yazdan@ut.ac.ir
Professor of Electrical Engineering
School of Electrical and Computer Eng., University of Tehran, Tehran, Iran
Office: Room #730, 7th floor, ECE Bldg.
Tel: 82084925
Email: yazdan@ut.ac.ir
Office hours
Students are welcome to set appointments through email.
Course Outline
Course Outline
● Introduction to Linear Algebra
● Sets, Relations, Functions, and Fields
● Abstract Algebra
● Vectors and Vector Spaces
● Bases and Dimension
● Linear Transformations
● Matrix Representation
● Inverse of Matrix
● Linear Operations
● Elementary Matrix Operations
● Gaussian Elimination
● Triangular Factorization
● LDU Decomposition
● Orthogonal Complement
● Dual Spaces
● Linear Functional
● (Non) Homogeneous / General Solutions
● Determinant
● Diagonalizability
● Matrix Limits and Markov Chains
● Invariant Subspaces
● Euclidean/Unitary/Hermitian Spaces
● QR Decomposition
● Least Square Approximation
● Symmetric/Definite Matrices
● Normal/Self-Adjoint Operators
● Spectral Theorem
● Approximation and Extremal Points
● Singular Value Decomposition
● Congruent Transformation
● Generalized Eigenvalue Problem
● Conditioning and Rayleigh Quotient
● Vector/Matrix Norms
● Jordan Canonical Form
● Introduction to Linear Algebra
● Sets, Relations, Functions, and Fields
● Abstract Algebra
● Vectors and Vector Spaces
● Bases and Dimension
● Linear Transformations
● Matrix Representation
● Inverse of Matrix
● Linear Operations
● Elementary Matrix Operations
● Gaussian Elimination
● Triangular Factorization
● LDU Decomposition
● Orthogonal Complement
● Dual Spaces
● Linear Functional
● (Non) Homogeneous / General Solutions
● Determinant
● Diagonalizability
● Matrix Limits and Markov Chains
● Invariant Subspaces
● Euclidean/Unitary/Hermitian Spaces
● QR Decomposition
● Least Square Approximation
● Symmetric/Definite Matrices
● Normal/Self-Adjoint Operators
● Spectral Theorem
● Approximation and Extremal Points
● Singular Value Decomposition
● Congruent Transformation
● Generalized Eigenvalue Problem
● Conditioning and Rayleigh Quotient
● Vector/Matrix Norms
● Jordan Canonical Form
References
Text book:
Friedberg, S. H., Insel, A. J. and Spence, L. E., Linear algebra, 4th Edition, Prentice Hall, 2002.
References:
CaBanerjee, S., and Anindya, R., Linear algebra and matrix analysis for statistics, CRC Press, 2014.
Strang, G., Introduction to Linear Algebra, 5th Edition, Wellesley-Cambridge Press, 2016.
Lipschutz, S., and Lipson, M. L., Linear Algebra: Schaum's Outlines, McGraw-Hill, 2009.
Bernstein, D. S., Matrix mathematics: theory, facts, and formulas, Princeton university press, 2009.
Gallier, J., Fundamentals of linear algebra and optimization, University of Pennsylvania 2014.
Chen, C. P., Linear Algebra. Lecture Notes.
Burl, J. B., Linear Optimal Control: H2 and H? Methods, Addison-Wesley Longman Publishing Co. Inc., 1998
Friedberg, S. H., Insel, A. J. and Spence, L. E., Linear algebra, 4th Edition, Prentice Hall, 2002.
References:
CaBanerjee, S., and Anindya, R., Linear algebra and matrix analysis for statistics, CRC Press, 2014.
Strang, G., Introduction to Linear Algebra, 5th Edition, Wellesley-Cambridge Press, 2016.
Lipschutz, S., and Lipson, M. L., Linear Algebra: Schaum's Outlines, McGraw-Hill, 2009.
Bernstein, D. S., Matrix mathematics: theory, facts, and formulas, Princeton university press, 2009.
Gallier, J., Fundamentals of linear algebra and optimization, University of Pennsylvania 2014.
Chen, C. P., Linear Algebra. Lecture Notes.
Burl, J. B., Linear Optimal Control: H2 and H? Methods, Addison-Wesley Longman Publishing Co. Inc., 1998
Assignments
Homeworks
Course Project
Goals
● To make students familiar with the new (applied/theoretical) emerging topics in the field.
● To improve research, technical reporting, and presentation abilities of students.
Preparation
● Students are supposed to select a topic and prepare a proposal. The proposal should be strictly related to the course syllabus.
● Prepare your proposal based on the specified format. (Use Adobe Acrobat Professional 8.0 or higher to open, fill out, save and print)
● Students should orally present their proposals, each in 5 minutes, at a presentations session (held at the last week of the term).
● Final reports should follow the standard template and are supposed to be submitted within 15 days after the final exam.
● Students should prepare their presentation file according to the standard template and then
present their final results, each in 15 minutes, at a session close to the deadline.
Suggestions
● Start your search for an appropriate topic from the first weeks of the course.
● Be in contact with the instructor about your topic of interest.
Important
● You should hand in a hard copy of your proposal at the presentations session.
● Avoid any kind of Plagiarism! Read IEEE Plagiarism Tutorial IEEE Plagiarism Tutorial carefully to know what plagiarism is and how to avoid it.
● Submission of the results of your research work, to any conference and/or journal, is primarily, subject to instructor's approval.
Evaluation of course project
Course Project
Goals
● To make students familiar with the new (applied/theoretical) emerging topics in the field.
● To improve research, technical reporting, and presentation abilities of students.
Preparation
● Students are supposed to select a topic and prepare a proposal. The proposal should be strictly related to the course syllabus.
● Prepare your proposal based on the specified format. (Use Adobe Acrobat Professional 8.0 or higher to open, fill out, save and print)
● Students should orally present their proposals, each in 5 minutes, at a presentations session (held at the last week of the term).
● Final reports should follow the standard template and are supposed to be submitted within 15 days after the final exam.
● Students should prepare their presentation file according to the standard template and then
present their final results, each in 15 minutes, at a session close to the deadline.
Suggestions
● Start your search for an appropriate topic from the first weeks of the course.
● Be in contact with the instructor about your topic of interest.
Important
● You should hand in a hard copy of your proposal at the presentations session.
● Avoid any kind of Plagiarism! Read IEEE Plagiarism Tutorial IEEE Plagiarism Tutorial carefully to know what plagiarism is and how to avoid it.
● Submission of the results of your research work, to any conference and/or journal, is primarily, subject to instructor's approval.
Evaluation of course project
| Evaluatin of Course Project | Percentage |
|---|---|
| Quality of report structure, format and appearance | 15% |
| Quality of oral presentation | 25% |
| Innovations, contributions, and depth of analysis/synthesis | 60% |
Evaluation
| Evaluatin of the Course | Percentage |
|---|---|
| Homeworks | 25% |
| Midterm Exam | 25% |
| Final Project | 25% |
| Final Exam | 25% |