Uploaded November 2022 | Updated September 2026, 2 weeks ago
It is only possible to perfectly diagonalize certain systems of linear differential equations. For the more general cases, it is possible to "block-diagonalize" the system into what is known as Jordan Canonical Form. This video explores these various options and derives the fully general Jordan form.
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 A tale of two "A" matrices
1:47 When it's possible to diagonalize a matrix with eigenvectors
6:15 Computing eigenvectors and generalized eigenvectors
20:03 Case of complex conjugate eigenvalues
23:10 Case of repeated eigenvalues
25:35 3x3 degenerate matrix
29:37 Jordan canonical form for general matrix
It is only possible to perfectly diagonalize certain systems of linear differential equations. For the more general cases, it is possible to "block-diagonalize" the system into what is known as Jordan Canonical Form. This video explores these various options and derives the fully general Jordan form.
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 A tale of two "A" matrices
1:47 When it's possible to diagonalize a matrix with eigenvectors
6:15 Computing eigenvectors and generalized eigenvectors
20:03 Case of complex conjugate eigenvalues
23:10 Case of repeated eigenvalues
25:35 3x3 degenerate matrix
29:37 Jordan canonical form for general matrix
![AI/ML+Physics Part 5: Employing an Optimization Algorithm [Physics Informed Machine Learning]](https://i.ytimg.com/vi/T4iJ10TAIMg/mqdefault.jpg "AI/ML+Physics Part 5: Employing an Optimization Algorithm [Physics Informed Machine Learning]
This video discusses the fifth stage of the machine learning process: (5) selecting and implementing an optimization algorithm to train the model. There are opportunities to incorporate physics into this stage of the process, such as using constrained optimization to force a model onto a susbpace or submanifold characterized by a symmetry or other physical constraint.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
01:45 Case Study: KKT Constrained Least Squares
06:18 Case Study: Physics Informed DMD
14:00 Loss vs Optimization of Subspace Constraints
17:50 Subspace Constraints and Symmetry
19:28 Case Study: Symbolic Regression and Evolutionary Optimization
22:25 Parsimony and Sparse Optimization Algorithms
25:03 Case Study: SINDy and SR3
28:38 Parsimony and Sparsity Hyperparameters
30:55 Outro")
![[6/8] Control for Societal-Scale Challenges: Road Map 2030 [Education]](https://i.ytimg.com/vi/VuAFZPwygyE/mqdefault.jpg "[6/8] Control for Societal-Scale Challenges: Road Map 2030 [Education]
This video explores the importance of education in realizing the ambitious goals of this road map document. This follows Chapter 6 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")
