Topic
Invariant factor
About: Invariant factor is a research topic. Over the lifetime, 40 publications have been published within this topic receiving 638 citations.
Papers
TL;DR: In this article, the existence of an n × n matrix over an arbitrary field when its invariant polynomials and either some rows or columns are prescribed is solved in terms of invariant factor inequalities and of majorization inequalities involving controllability indices and the degrees of the invariants.
125 citations
1 Jan 1994
TL;DR: The main purpose of this paper is to show how the so-called input-output controllable models can be constructed in a an easy-to-implement, recursive way.
Abstract: The approach to modeling inspired by the behavioral framework consists in treating all measurements on an equal footing, not distinguishing between inputs and outputs. Consequently, the initial search is for autonomous models. In the linear, time invariant case, the main result guarantees the existence of a minimal complexity autonomous generating model Θ*. This means that all other models can be explicitely constructed from Θ*. Among them in most cases, the so-called input-output controllable models are of interest. The main purpose of this paper is to show how these models can be constructed in a an easy-to-implement, recursive way.
42 citations
TL;DR: In this article, the authors show some connections between pole assignment in control theory and assignment of invariant factors on matrices with some prescribed submatrices and show that the majorization in the Hardy-Littlewood-Polya sense and the interlacing inequalities for invariants play a fundamental role in the solution of some problems common to both theories.
29 citations
23 citations
TL;DR: Using Goursat's lemma for groups, a simple representation and the invariant factor decompositions of the subgroups of the group $\mathbb{Z}_m \times ǫ n$ are deduced, where $m$ and $n$ are arbitrary positive integers as discussed by the authors.
Abstract: Using Goursat’s lemma for groups, a simple representation and the invariant factor decompositions of the subgroups of the group $\mathbb{Z}_m \times \mathbb{Z}_n$ are deduced, where $m$ and $n$ are arbitrary positive integers. As consequences, explicit formulas for the total number of subgroups, the number of subgroups with a given invariant factor decomposition, and the number of subgroups of a given order are obtained.
21 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2020 | 1 |
| 2019 | 2 |
| 2017 | 1 |
| 2016 | 1 |
| 2014 | 2 |