Lecture
This lecture covers the reduction of a linear transformation in a 2-dimensional space, aiming to find a simpler matrix representation. The instructor explains the motivation behind this reduction process and introduces the concept of a 'simple' matrix. The lecture progresses to discuss the Jordan form and diagonalizability of matrices, illustrating examples and properties of characteristic polynomials and eigenvalues. The presentation concludes with the concept of eigenvectors and projections in the context of matrix reduction.