Linear Algebra
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This course is the second of a two-term sequence. The focus is on coding techniques for approaching the Shannon limit of additive white Gaussian noise (AWGN) channels, their performance analysis, and design principles. After a review of Principles of Digital Communication I and the Shannon limit for AWGN channels, the course begins by discussing small signal constellations, performance analysis and coding gain, and hard-decision and
This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.
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Concentrates on recognizing and solving convex optimization problems that arise in engineering. Topics include: Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interiorpoint methods. Applications to signal...more
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Videos on pre-algebra. Should be ready for the "Algebra" playlist if you understand everything here.
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180 Worked Algebra I examples (problems written by the Monterey Institute of Technology and Education). You should look at the "Algebra" playlist if you've never seen algebra before or if you want instruction on topics in Algebra II. Use this playlist to see a ton of example problems in every topic in the California Algebra I Standards. If you can do all of these problems on your own, you should probably test out of Algebra I (seriously).
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Topics covered from very basic algebra all the way through algebra II. This is the best algebra playlist to start at if you've never seen algebra before. Once you get your feet wet, you may want to try some of the videos in the "Algebra I Worked Examples" playlist.
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Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix...more
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This is a basic course on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
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Addendum: Hit-And-Run CG Algorithm, Maximum Volume Ellipsoid Method, Chebyshev Center Method, Analytic Center Cutting-Plane Method, Extensions (Of Cutting-Plane Methods), Dropping Constraints, Epigraph Cutting-Plane Method, PWL Lower Bound On Convex Function, Lower Bound, Analytic Center Cutting-Plane Method, ACCPM Algorithm, Constructing Cutting-Planes, Computing The Analytic Center, Infeasible Start Newton Method Algorithm, Properties...more
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Recap: Example: Minimum Cardinality Problem, Interpretation As Convex Relaxation, Interpretation Via Convex Envelope, Weighted And Asymmetric L_1 Heuristics, Regressor Selection, Sparse Signal Reconstruction, L_1-Norm Methods For Convex-Cardinality Problems Part II, Total Variation Reconstruction, Total Variation Reconstruction, TV Reconstruction, L_2 Reconstruction, Iterated Weighted L_1 Heuristic, Sparse Solution Of Linear Inequalities,...more
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Selection Sort, Live Demo: Working/execution of the Code, Selection Sort Analysis, Insertion Sort Algorithm, Live Demo: Working/execution of Insertion Sort, Insertion Sort Analysis, Insertion vs Selection, Quadratic Growth of the Algorithm, Merge Sort, Merge Sort: Working/execution Demo, Merge Sort Code Explanation, Merge Sort Analysis, Quadratic vs Linear Arithmetic, Sort 'Race', Quick Sort Idea
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Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error Minimization, Localization And Cutting-Plane Methods, Cutting-Plane Oracle, Neutral And Deep Cuts, Unconstrained Minimization, Deep Cut For Unconstrained Minimization, Feasibility Problem, Inequality...more
