Jordan Canonical Form ( JCF) is one of the most important, and useful, concepts in linear algebra. In this book we develop JCF and show how to apply it to solving systems of differential equations. We first develop JCF, including the concepts involved in it–eigenvalues, eigenvectors, and chains of generalized eigenvectors.We begin with the diagonalizable case and then proceed to the general cas...

In this paper we discuss algorithmic aspects of the computation of the Jordan canonical form. Inspired by the Golub & Wilkinson paper 9] on the computation of the Jordan canonical form, an O(n 3) algorithm was developed by Beelen & Van Dooren 3] for computing the Kronecker structure of an arbitrary pencil B ? A. Here we show how the ideas of this algorithm lead to a special algorithm for recons...

A proof of the Jordan canonical form, suitable for a first course in linear algebra, is given. The proof includes the uniqueness of the number and sizes of the Jordan blocks. The value of the customary procedure for finding the block generators is also questioned. 2000 MSC: 15A21. The Jordan form of linear transformations is an exceeding useful result in all theoretical considerations regarding...

The Jordan canonical form (JCF) of a square matrix is a foundational tool in matrix analysis. If the matrix A is known exactly, symbolic computation of the JCF is possible though expensive. When the matrix contains parameters, exact computation requires either a potentially very expensive case discussion, significant expression swell or both. For this reason, no current computer algebra system ...

In this paper we use preferred and quasi-preferred bases of generalized eigenspaces associated with the spectral radius of nonnegative matrices to analyze the existence and uniqueness of a variant of the Jordan canonical form which we call FrobeniusJordan form. It is a combination of the classical Jordan canonical form in the part associated with the eigenvalues that are different from the spec...