# Jaimie Swartz

I started graduate school without having taken a full linear algebra course, and struggled with the material I saw in controls and optimization in my first year of grad school. It was through repeated exposure of this kind of material and finding resources that described the material from different perspectives that I started to really understand what it was and why it was useful. Below I have a short list of resources I think are the most critical to getting a solid understanding, and below that is a dropdown of a long list of resources that is catergorized by linear systems topic. Hope this is useful to other student researchers in the field.

## Linear Systems Resources - Short List

Texts
Linear Algebra Done Right linear.axler.net Helps build conceptual understanding of linear algebra (subspaces, eigenvalues, etc.)
What and Why Mathematical Proofs www2.math.uconn.edu/~hurley/math315/proofgoldberger.pdf Review of direct, contradition, and induction style of proving theorems
Video series
Blue1Brown - Linear Algebra Series www.youtube.com/c/3blue1brown/playlistswww.youtube.com/c/3blue1brown/playlists?view=50&sort=dd&shelf_id=20 Builds visual intuition for linear algebra concepts
Professor Claire Tomlin - Linear Systems Recorded Lectures www.youtube.com/playlist?list=PLrmdED6yqL3UImn8cJtrBDuoye9QKJ9MJ The Lectures of UC Berkeley EE221A Linear Systems
Professor Steve Brunton - Control Bootcamp www.youtube.com/playlist?list=PLMrJAkhIeNNR20Mz-VpzgfQs5zrYi085m Professor Brunton has many playlists related to control and dynamical systems, but I in particular loved the control bootcamp
Websites
Interactive plotter of LTI system phase portraits mathlets.org/mathlets/linear-phase-portraits-matrix-entry/ Useful to bookmark for checking the trajectory behavior of 2D LTI systens
Interactive plotter of 2D (potentially nonlinear) phase planes aeb019.hosted.uark.edu/pplane.html Useful to check trajectory of nonlinear systems without breaking out any code