Stanford / Engineering / Electrical
Lecture : Gain Of A Matrix In A Direction
By Stephen Boyd | Introduction to Linear Dynamical Systems
Lecture 17 of 20
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Course Description
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 exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. Control, reachability, state transfer, and least-norm inputs. Observability and least-squares state estimation.

Prerequisites: Exposure to linear algebra and matrices (as in Math. 103). You should have seen the following topics: matrices and vectors, (introductory) linear algebra; differential equations, Laplace transform, transfer functions. Exposure to topics such as control systems, circuits, signals and systems, or dynamics is not required, but can increase your appreciation.
Courses Index
1 : Advanced Topics in Circuit Design   (Elad Alon / Berkeley)
2 : Introduction to Digital Integrated Circuits   (Jan RABAEY / Berkeley)
3 : Advanced Analog Integrated Circuits   (Elad Alon / Berkeley)
4 : Introduction to Microelectronic Circuits   (Bernhard BOSER / Berkeley)
5 : The Fourier Transform and its Applications   (Brad Osgood / Stanford)
6 : Convex Optimization I   (Stephen Boyd / Stanford)
7 : Convex Optimization II   (Stephen Boyd / Stanford)
8 : Circuits and Electronics   (Anant Agarwal / MIT)
9 : Computer System Engineering   (Samuel Madden / MIT)
10 : Introduction to Algorithms   (Erik Demaine / MIT)
11 : Principles of Digital Communications I   (Lizhong Zheng / MIT)
12 : Principles of Digital Communication II   (David Forney / MIT)
13 : Understanding Lasers and Fiberoptics   (Shaoul Ezekiel / MIT)
14 : Electromagnetics and Applications   (Multiple Instructors / MIT)
15 : Information and Entropy   (Paul Penfield / MIT)
16 : Fundamentals of Laser   (Sabieh Anwar / LUMS)
17 : Synchrotron Radiation for Materials Science   (David Attwood / Berkeley)
18 : Linear Integrated Circuits   (Clark Nguyen / Berkeley)
19 : Digital Circuit Design   (Ken Boyd / University of New South Wales)
20 : Speech and Audio Processing   (Multiple Multiple / University of New South Wales)