Uploaded October 2022 | Updated September 2026, 2 weeks ago
This video explores the eigenvalues and eigenvectors of a matrix "A". This is one of the most important concepts in linear algebra. The eigenvectors represent a change of coordinates in which the "A" matrix becomes diagonal, with entries given by the eigenvalues. This allows us to easily solve arbitrarily complex linear systems of differential equations.
Playlist: youtube.com/playlist?list=PLMrJAkhIeNNTYaOnVI3QpH7jgULnAmvPA
Course Website: http://faculty.washington.edu/sbrunton/me564/
@eigensteve on Twitter
eigensteve.com
databookuw.com
This video was produced at the University of Washington
%%% CHAPTERS %%%
0:00 Overview and Eigenvalue Equation
3:15 Eigenvalues and Eigenvectors are "Special"
6:00 Example 2x2 Matrix
14:55 Computing Eigenvalues and Eigenvectors for *any* Matrix
21:18 The Determinant Measures Area of a Transformation
25:50 Determinant of 3x3 Matrix
28:35 Revisit 2x2 Matrix Example
This video explores the eigenvalues and eigenvectors of a matrix "A". This is one of the most important concepts in linear algebra. The eigenvectors represent a change of coordinates in which the "A" matrix becomes diagonal, with entries given by the eigenvalues. This allows us to easily solve arbitrarily complex linear systems of differential equations.
Playlist: youtube.com/playlist?list=PLMrJAkhIeNNTYaOnVI3QpH7jgULnAmvPA
Course Website: http://faculty.washington.edu/sbrunton/me564/
@eigensteve on Twitter
eigensteve.com
databookuw.com
This video was produced at the University of Washington
%%% CHAPTERS %%%
0:00 Overview and Eigenvalue Equation
3:15 Eigenvalues and Eigenvectors are "Special"
6:00 Example 2x2 Matrix
14:55 Computing Eigenvalues and Eigenvectors for *any* Matrix
21:18 The Determinant Measures Area of a Transformation
25:50 Determinant of 3x3 Matrix
28:35 Revisit 2x2 Matrix Example
![AI/ML+Physics: Preview of Upcoming Modules and Bootcamps [Physics Informed Machine Learning]](https://i.ytimg.com/vi/_ObvDgPMWkU/mqdefault.jpg "AI/ML+Physics: Preview of Upcoming Modules and Bootcamps [Physics Informed Machine Learning]
This video provides a brief preview of the upcoming modules and bootcamps in this series on Physics Informed Machine Learning. Topics include: (1) Parsimonious modeling and SINDy; (2) Physics informed neural networks (PINNs); (3) Operator methods, like DeepONets and Fourier Neural Operators; (4) Symmetries in physics and machine learning; (5) Digital Twin technology; and (6) Case studies in engineering.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro & Recap
01:06 Reviewing the 5 Stages
04:08 Reviewing Physics in the Stages
05:11 Why Physical Models: Cost & Data Scale
07:53 Why Physical Models: Generalized Models
10:01 Why Physcial Models: Discovering Physics
11:40 Holistic Impact of Embedding Physics // Struggling to find a good wording here
12:55 Case Study: Pendulum Data and SINDy
15:20 Case Study: Symbolic Regression and Evolutionary Optimization
16:45 Case Study: Lagrangian Neural Networks
18:34 Architectures and Symmetries
19:36 Applications in Engineering
21:21 The Digital Twin
22:15 Benchmark Problems
23:35 Outro")
![[7/8] Control for Societal-Scale Challenges: Road Map 2030 [Ethics, Fairness, & Regulatory Issues]](https://i.ytimg.com/vi/aOiAsphMsCI/mqdefault.jpg "[7/8] Control for Societal-Scale Challenges: Road Map 2030 [Ethics, Fairness, & Regulatory Issues]
This video explores ethics, fairness, and regulatory issues associated with applying control to solve these major societal challenges. This follows Chapter 7 of the Control for Societal-Scale Challenges: Road Map 2030 document.
https://www.ieeecss.org/control-societal-scale-challenges-road-map-2030
The production of this video was supported by the IFAC.
Roadmap Abstract: The world faces some of its greatest challenges of modern time and how we address them will have a dramatic impact on the life for generations to come. Simultaneously, control systems, consisting of information enriched by various degrees of analytics followed by decision-making, are pervading a variety of sectors, not only in engineering but beyond, into financial services, socio-economic analysis, entertainment and sports, and political and social sciences. Increased levels of automation are sought after in various sectors and being introduced into new domains. All of these advances and transformations urge a shift in the conversation toward how control systems can meet grand societal- scale challenges. The document seeks to chart a roadmap for the evolution of control systems, identifying several areas where our discipline can have an impact over the next decade.
Edited by: Anuradha M. Annaswamy, Karl H. Johansson, and George J. Pappas
Authors: Andrew Alleyne, Frank Allgöwer, Aaron D. Ames, Saurabh Amin, James Anderson, Anuradha M. Annaswamy, Panos J. Antsaklis, Neda Bagheri, Hamsa Balakrishnan, Bassam Bamieh, John Baras, Margret Bauer, Alexandre Bayen, Paul Bogdan, Steven L. Brunton, Francesco Bullo, Etienne Burdet, Joel Burdick, Laurent Burlion, Carlos Canudas de Wit, Ming Cao, Christos G. Cassandras, Aranya Chakrabortty, Giacomo Como, Marie Csete, Fabrizio Dabbene, Munther Dahleh, Amritam Das, Eyal Dassau, Claudio De Persis, Mario di Bernardo, Stefano Di Cairano, Dimos V. Dimarogonas, Florian Dörfler, John C. Doyle, Francis J. Doyle III, Anca Dragan, Magnus Egerstedt, Johan Eker, Sarah Fay, Dimitar Filev, Angela Fontan, Elisa Franco, Masayuki Fujita, Mario Garcia-Sanz, Dennice Gayme, Wilhelmus P.M.H. Heemels, João P. Hespanha, Sandra Hirche, Anette Hosoi, Jonathan P. How, Gabriela Hug, Marija Ilić, Hideaki Ishii, Ali Jadbabaie, Matin Jafarian, Samuel Qing-Shan Jia, Tor Arne Johansen, Karl H. Johansson, Dalton Jones, Mustafa Khammash, Pramod Khargonekar, Mykel J. Kochenderfer, Andreas Krause, Anthony Kuh, Dana Kulić, Françoise Lamnabhi-Lagarrigue, Naomi E. Leonard, Frederick Leve, Na Li, Steven Low, John Lygeros, Iven Mareels, Sonia Martinez, Nikolai Matni, Tommaso Menara, Katja Mombaur, Kevin Moore, Richard Murray, Toru Namerikawa, Angelia Nedich, Sandeep Neema, Mariana Netto, Timothy O’Leary, Marcia K. O’Malley, Lucy Y. Pao, Antonis Papachristodoulou, George J. Pappas, Philip E. Paré, Thomas Parisini, Fabio Pasqualetti, Marco Pavone, Akshay Rajhans, Gireeja Ranade, Anders Rantzer, Lillian Ratliff, J. Anthony Rossiter, Dorsa Sadigh, Tariq Samad, Henrik Sandberg, Sri Sarma, Luca Schenato, Jacquelien Scherpen, Angela Schoellig, Rodolphe Sepulchre, Jeff Shamma, Robert Shorten, Bruno Sinopoli, Koushil Sreenath, Jakob Stoustrup, Jing Sun, Paulo Tabuada, Emma Tegling, Dawn Tilbury, Claire J. Tomlin, Jana Tumova, Kevin Wise, Dan Work, Junaid Zafar, Melanie Zeilinger
This video was produced at the University of Washington")
