Matrix Representation of Operators and Basis Transformation

This lecture covers the matrix representation of operators in a basis, where a linear operator on a vector space is represented by a matrix. It also delves into the basis transformation of vectors and operators, focusing on the relationship between different bases and the corresponding matrices. The instructor explains how to represent vectors and operators in an arbitrary orthonormal basis, emphasizing the importance of unitary matrices and the properties of self-adjoint and normal operators.