Matrix Eigenvalues and Eigenvectors

This lecture covers the solution to exercise number six, focusing on proving that the inverse of a matrix A has the same eigenvalue as A itself, and that the transposed version of A shares the same set of eigenvalues. Through detailed explanations and examples, the instructor demonstrates how to calculate characteristic polynomials, determine eigenvalues, and find eigenvectors for both A and A transposed, ultimately showing that while they may have the same eigenvalues, they can have different sets of eigenvectors.