Linear Algebra: Matrix Representation of Linear Applications

This lecture covers the process of finding a matrix associated with a linear application from one vector space to another, focusing on the representation in known cases of Rn and Rm. The instructor explains how to find the matrix representation in different bases, using examples to illustrate the concept. The lecture also delves into the importance of eigenvalues and eigenvectors, showcasing how they are crucial in solving dynamic systems. Additionally, the instructor discusses the characteristic polynomial, trace, and determinant of a matrix, providing insights into how they can be used to calculate eigenvalues efficiently.