Here is a great way to learn how to use linear algebra: https://web.stanford.edu/~boyd/vmls/
Computational Linear Algebra. A first-year undergraduate course thanks to the University of Michigan Robotics Institute
If you prefer a classic: https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/
The best reference for applied convex optimization http://web.stanford.edu/~boyd/cvxbook/ Make sure to check the VMLS book before tackling this content. The video lectures are the closest that a lecture could get to a TV show, they are super engaging https://www.youtube.com/playlist?list=PL3940DD956CDF0622
The lecture notes from professor Ahmadi. http://aaa.princeton.edu/orf523
If you prefer a robust taste, the book from Ben-Tal, El Ghaoui and Nemirovski is very well written https://www2.isye.gatech.edu/~nemirovs/FullBookDec11.pdf
This video tutorial Matthew Kelly in Trajectory Optimization. https://www.youtube.com/watch?v=wlkRYMVUZTs
Here is the paper that summarizes the video tutorial http://www.matthewpeterkelly.com/research/MatthewKelly_IntroTrajectoryOptimization_SIAM_Review_2017.pdf
Professor Tedrake's class puts everything into context: control, optimization, and robotics! The lecture notes and videos are updated and constitute an excellent resource. Now that we are here, the Professor Tedrake's interview with Lex Fridman is also recommended.
Here is a reference on how to apply optimization into control synthesis, not only for robot control. Linear Matrix Inequalities in System and Control Theory
From one of the founders of HEBI robotics. https://youtu.be/jC9uPyXPAFo
A peer-reviewed portrait of suffering, The Atlantic. How can the state-of-the-art rehabilitation robots improve the quality of life for Liviana Sulzer? This is an emotional story that reveals important weaknesses designing wearable technology.
Exoskeleton prototype development story - Enhanced Robotics From the respected and disciplined Hanqi Zhu (Leon)
This is not free but it is a great resource: Biomechanics and Motor Control of Human Movement, Winter, D.A.
Just some of the many research laboratories with great work:
Machine Interface Systems Team - Houston, TX -Jose Luis Contreras-Vidal
Stanford Biomechatronics Laboratory - Stanford, CA - Steve Collins
Locomotor Control Systems Laboratory - Ann Arbor, MI - Robert D. Gregg
Biomechatronics - Cambridge, MA - Hugh Herr (Augmented - PBS Documentary for context)
Center for Intelligent Mechatronics - Nashville, TN, - Michael Goldfarb
Neuromuscular Rehabilitation Engineering Laboratory - Chapel Hill, NC - He (Helen) Huang
Biomechanics & Assistive Technology Laboratory - Nashville, TN - Karl Zelik
Berkeley Robotics & Human Engineering Laboratory - Berkeley, CA - Homayoon Kazerooni
Physiology of Wearable Robotics Laboratory, Atlanta, GA - Gregory Sawicki
...
Great YouTube playlist from Brock Laschowski.
Dimitris Bertsimas' philosophy, from Professor Bertsimas.
Doing it my way from Dr. Jean-luc Doumont
What are we optimizing: short-term sum or long-term max? from Professor Daniel Liberzon
Surviving the Review Process from Professor Set Hutchinson
Graduate student advice: Humble Beginnings & Scientific Writing from Professor Jessy Grizzle (Note to myself: 13:38)
Graduate student advice from Professor Nima Fazeli
English communication for scientists from Dr. Jean-luc Doumont
The Awesomest 7-Year Postdoc from Professor Radhika Nagpal. (Thanks to Jim and Jessy)
Mentor the Researcher, Not the Research: An Essay on PhD Mentoring from Professor George J. Pappas