Jordan normal form

Jordan normal form is a way of representing matrices in linear algebra to simplify complex linear transformations. It organizes a matrix into blocks, making it easier to understand the structure of its eigenvalues and eigenvectors. Each block corresponds to an eigenvalue and shows how it affects the transformation. This form helps mathematicians and scientists analyze systems, solve differential equations, and study stability by revealing the essential properties of the matrix without losing important information. Essentially, it provides a clearer picture of how a linear system behaves.