Jordan blocks

Jordan blocks are a mathematical concept used in linear algebra to represent certain matrices, especially when they aren’t diagonalizable. They are structured matrices that help simplify complex systems by organizing their behavior into manageable parts. Think of a Jordan block as a compact way to capture both the eigenvalues (which describe natural behaviors) and the way systems slightly deviate from simple behaviors through generalized vectors. This structure is fundamental in understanding how matrices act on spaces, particularly when systems are close to, but not exactly, diagonalizable.