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 common problem in frequent graph mining is the size of the output, which can easily exceed the size of the database to analyze. In the application area of molecular fragment mining a promising approach to tackle this problem is to treat certain substructures as a unit. Among such structures, rings are most prominent, and by requiring that either a ring is present as a whole in a fragment, or ...

In frequent subgraph mining one tries to find all subgraphs that occur with a user-specified minimum frequency in a given graph database. The basic approach is to grow subgraphs, adding an edge and maybe a node in each step, to count the number of database graphs containing them, and to eliminate infrequent subgraphs. The predominant method to avoid redundant search (the same subgraph can be gr...

A canonical form for circuit diagrams with a designated start state is presented. The form is based upon nite automata minimization and Shannon's canonical form for boolean expressions.

Given a linear time-invariant control system, it is well known that the transmission zeroes are the generalized eigenvalues of a matrix pencil. Adding outputs to place additional zeroes is equivalent to appending rows to this pencil to place new generalized eigenvalues. Adding inputs is likewise equivalent to appending columns. Since both problems are dual to each other, we only show in this pa...