Eigenvalues Reduction: Two Real Eigenvalues

This lecture covers the reduction of a matrix A to a simpler form based on its eigenvalues. By analyzing the discriminant A₁, one can determine the type of matrix 'simple' that A can be transformed into. The case where A₁ is greater than 0, indicating two real eigenvalues, is explored in detail. The process involves finding an invertible matrix P that diagonalizes A, leading to a simpler form. Examples are provided to illustrate the concept of diagonalizability and the associated eigenvectors.