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Lecture 1 | 01:16:46 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, gives an overview of the course, Introduction to Linear Dynamical Systems (EE263).Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. | |||
Lecture 2 | 01:05:52 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on linear functions for the course, Introduction to Linear Dynamical Systems (EE263).Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. | |||
Lecture 3 | 01:19:11 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, gives a review of linear algebra for the course, Introduction to Linear Dynamical Systems (EE263).Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. | |||
Lecture 4 | 01:14:08 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on orthonormal sets of vectors and QR factorization for the course, Introduction to Linear Dynamical Systems (EE263).Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. | |||
Lecture 5 | 01:15:14 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on QR factorization and least squares for the course, Introduction to Linear Dynamical Systems (EE263).Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. | |||
Lecture 6 | 01:16:19 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on the applications of least squares for the course, Introduction to Linear Dynamical Systems (EE263).Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. | |||
Lecture 7 | 01:15:46 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on regularized least squares and the Gauss-Newton method for the course, Introduction to Linear Dynamical Systems (EE263).Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. | |||
Lecture 8 | 01:15:58 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on the least norm solutions of undetermined equations for the course, Introduction to Linear Dynamical Systems (EE263).Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. | |||
Lecture 9 | 01:09:02 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on autonomous linear dynamical systems for the course, Introduction to Linear Dynamical Systems (EE263).Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. | |||
Lecture 10 | 01:11:42 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on autonomous linear dynamical systems and how they relate to Electrical Engineering for the course, Introduction to Linear Dynamical Systems (EE263).Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution. | |||
Lecture 11 | 01:08:55 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on how to find solutions via LaPlace transform and the use of matrix exponentials for the course, Introduction to Linear Dynamical Systems (EE263). Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution. | |||
Lecture 12 | 01:13:37 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on matrix exponentials, eigenvectors, and diagonalization and their uses in LDS for the course, Introduction to Linear Dynamical Systems (EE263). Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices. | |||
Lecture 13 | 01:13:01 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on generalized eigenvectors, diagonalization, and Jordan canonical form for the course, Introduction to Linear Dynamical Systems (EE263).Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution. | |||
Lecture 14 | 01:17:42 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on the applications of Jordan canonical form in LDS and electrical engineering for the course, Introduction to Linear Dynamical Systems (EE263).Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution. | |||
Lecture 15 | 01:09:01 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on inputs and outputs of linear dynamical systems, as well as symmetric matrices for the course, Introduction to Linear Dynamical Systems (EE263).Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution. | |||
Lecture 16 | 01:12:35 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on the use of symmetric matrices, quadratic forms, matrix norm, and SVDs in LDS for the course Introduction to Linear Dynamical Systems (EE263). Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution. | |||
Lecture 17 | 01:16:52 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on the use of symmetric matrices, quadratic forms, matrix norm, and SVDs in LDS for the course Introduction to Linear Dynamical Systems (EE263). Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution. | |||
Lecture 18 | 01:15:14 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on the applications of SVD, controllability, and state transfer in electrical engineering for the course, Introduction to Linear Dynamical Systems (EE263). Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution. | |||
Lecture 19 | 01:10:30 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on controllability and state transfer and their uses in modern electrical engineering for the course, Introduction to Linear Dynamical Systems (EE263). Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution. | |||
Lecture 20 | 01:09:25 | ||
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, gives his final lecture on observability and state estimation for the course, Introduction to Linear Dynamical Systems (EE263). Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations 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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution. |
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