Linear algebra is used to solve various optimization problems. Basic concepts in Linear algebra include vectors, vector space, linear transformations, systems of linear equations. While optimization problems can be linear or non linear.
Vectors:
Reference:
C. C. Aggarwal, Linear Algebra and Optimization for Machine Learning: A Textbook. Cham: Springer International Publishing, 2020. doi: 10.1007/978-3-030-40344-7.
Y. Geophys, “Basic concepts in Linear Algebra and Optimization,” [Online]. Available: https://stanford.edu/~yinbin/TEACHING/Optimization.pdf