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.

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 |