Jordan Canonical Form: Theory and Practice
نویسنده
چکیده
منابع مشابه
Infinite-dimensional versions of the primary, cyclic and Jordan decompositions
The famous primary and cyclic decomposition theorems along with the tightly related rational and Jordan canonical forms are extended to linear spaces of infinite dimensions with counterexamples showing the scope of extensions.
متن کاملLecture 4: Jordan Canonical Forms
This lecture introduces the Jordan canonical form of a matrix — we prove that every square matrix is equivalent to a (essentially) unique Jordan matrix and we give a method to derive the latter. We also introduce the notion of minimal polynomial and we point out how to obtain it from the Jordan canonical form. Finally, we make an encounter with companion matrices. 1 Jordan form and an applicati...
متن کاملNUROP Congress Paper Jordan Canonical Forms of Linear Operators
Any linear transformation can be represented by its matrix representation. In an ideal situation, all linear operators can be represented by a diagonal matrix. However, in the real world, there exist many linear operators that are not diagonalizable. This gives rise to the need for developing a system to provide a beautiful matrix representation for a linear operator that is not diagonalizable....
متن کاملHow to Find Bases for Jordan Canonical Forms
The idea for nding a basis relates to the proof of why a Jordan canonical form exists. What we seek to do is nd a largest possible set of chains (or cycles) of the form {x, (T −λkI)(x), . . . , (T −λkI)(x)} which are linearly independent. By the proof of Jordan canonical form, the number and lengths of these chains can be found from the numbers d0, . . . , d`k . Indeed, let λ = λk be a xed eige...
متن کاملComputational Aspects of the Jordan Canonical Form
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...
متن کامل