This article presents basic notions of Lie theory in the context of matrix groups with goals of minimizing the required mathematical background and maximizing accessibility. It is structured with exercises that enhance the text and make the notes suitable for (part of) an introductory course at the upper level undergraduate or early graduate level. Indeed the notes were originally written as part of an introductory course to geometric control theory.
"Matrix Lie Groups: An Introduction." J. Gen. Lie Theory Appl. 9 (2) 1 - 9, 2015. https://doi.org/10.4172/1736-4337.1000229