Diagonal canonical form of interval matrices and applications on dynamical systems

Abstract

Finding the simplest form of a set of quantities is an important aspect of any branch of Mathematics. Of course, the simplest form or the canonical form as we often call it in mathematics, must possess all the important characteristics of the set of quantities. A real square matrix satisfying certain conditions can be brought to diagonal form which is its simplest form such that the diagonal form retains the eigenvalues, determinants, trace, rank, nullity,.. of the original matrix.
Many computations with matrices become easier if one can diagonalize the matrices. In this article, we suggest an approach for diagonalizing interval matrices employing a novel methodology called the pairing technique, which will make it simpler and more effective to classify and investigate interval matrices. This is extremely useful because computations involving a diagonalizable matrix can often be reduced to much simpler computations involving the corresponding diagonal matrix. We also discuss two real world applications on planar systems and linear discrete dynamical systems.