Linear Algebra in 3 Dimensions: Change of Bases

This lecture covers the concept of changing bases in linear algebra in 3 dimensions, focusing on the transformation of matrices and vectors between different bases. The instructor explains the process of expressing linear transformations in terms of new bases and provides proofs and examples to illustrate the theoretical concepts. Key topics include the definition of linear applications, the use of matrices to represent transformations, and the importance of understanding bases for determining linear independence. Through detailed explanations and mathematical demonstrations, students will gain a solid understanding of how to navigate and manipulate vectors and matrices in different bases.