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COURSE DESCRIPTION: This course proposes fundamentals of Linear algebra and its applications. Topics to be covered consist of: Basic Matrix Algebra 1. Linear equations, pivoting, LU factorizations, determinants, General vector spaces 1. Definitions, sums and direct sums, subspaces, bases, span, dimension, 2. Linear maps, range and null spaces, matrix of linear maps, invariant subspaces, 3. Inner-product spaces, operators, norms, orthogonal projections, optimization problems, linear functionals and adjoints, 4. Operators, self adjoint, normal and positive operators, isometries, singular value decomposition, Square roots, 5. Jordan forms, 6. Trace and determinant of operators,
Applications 1. Least squares problems, 2. Linear dynamical systems, similarity transformation, internal stability, 3. Introduction to convex optimization.
_______________________________________________________ GRADING: 1. Assignments: 10% (if average of midterm and final exam > 11) 2. Mid-term exam: 40% 3. Final exam: 50% _______________________________________________________ REFERENCES: 1. S. Axler, Linear algebra done right, 2nd edition, Springer, 1997 (SEE) (main textbook) 2. G. Strang, Linear algebra and its applications, 4th edition, Pearson, 2011 (SEE) 3. G.H. Golub, C.F. Van Loan, Matrix computations, 4th Edition, John Hopkins university press, 2013 4. N. Loehr, Advanced linear algebra, Taylor and Francis (CRC) press, 2014 5. M. Green and D. Limebeer, "Linear robust control", Prentice Hall, 1995 |
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Control systems are ubiquitous |
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Sharif university of technology Department of electrical engineering Digital systems group/Robotics
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Linear Algebra Fall 2016-7 Credits: 3 Level: Undergrad. Prerequisite: Calculus 1,2 Hours: Saturday, Monday, 2 to 3:30pm Location: |
