Linear Algebra
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Jordan Canonical Form, Generalized Modes, Cayley-Hamilton Theorem, Proof Of C-H Theorem, Linear Dynamical Systems With Inputs & Outputs, Block Diagram, Transfer Matrix, Impulse Matrix, Step Matrix
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Continue On Experiment Design, Geometric Problems, Minimum Volume Ellipsoid Around A Set, Maximum Volume Inscribed Ellipsoid, Efficiency Of Ellipsoidal Approximations, Centering, Analytic Center Of A Set Of Inequalities, Linear Discrimination
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Multinomial Event Model, Non-linear Classifiers, Neural Network, Applications of Neural Network, Intuitions about Support Vector Machine (SVM), Notation for SVM, Functional and Geometric Margins
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Least-Norm Solution, Least-Norm Solution Via QR Factorization, Derivation Via Langrange Multipliers, Example: Transferring Mass Unit Distance, Relation To Regularized Least-Squares, General Norm Minimization With Equality Constraints, Autonomous Linear Dynamical Systems, Block Diagram
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Scheinman Arm - Demo, Kinematic Singularity, Example - Kinematic Singularity, Puma Simulation, Resolved Rate Motion Control, Angular/Linear - Velocities/Forces, Velocity/Force Duality, Virtual Work, Example
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Lagrangian, Lagrange Dual Function, Least-Norm Solution Of Linear Equations, Standard Form LP, Two-Way Partitioning, Dual Problem, Weak And Strong Duality, Slater's Constraint Qualification, Inequality Form LP, Quadratic Program, Complementary Slackness
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Introduction, Examples, Solving Optimization Problems, Least-Squares, Linear Programming, Convex Optimizations, How To Solve?, Course Goals
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Kernels, Mercer's Theorem, Non-linear Decision Boundaries and Soft Margin SVM, Coordinate Ascent Algorithm, The Sequential Minimization Optimization (SMO) Algorithm, Applications of SVM
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Newton's Method, Exponential Family, Bernoulli Example, Gaussian Example, General Linear Models (GLMs), Multinomial Example, Softmax Regression
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Validating simulation results, curve fitting, linear regression
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Using the method of undetermined coefficients to solve nonhomogeneous linear differential equations.
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