On the characteristic polynomial of matrices with prescribed columns and the stabilization and observability of linear systems

• Type: Article in International Scientific Journal
• Date: 1998

Authors

Susana Margarida Figueiredo de Sousa Borges Furtado (Author) FEP; Fernando Silva (Author) Other

Journal

Title: Electronic Journal of Linear Algebra

Vol. 4

Pages: 19-31

ISSN: 1537-9582

Publisher: INT LINEAR ALGEBRA SOC

Indexing

ISI Web of Science

Scopus - 3 Citations

Scientific classification

FOS: Natural sciences

Other information

Authenticus ID: P-007-BWM

Abstract (EN): Let A ¿ FnXn, B ¿ FnXt, where F is an arbitrary field. In this paper, the possible characteristic polynomials of [A B], when some of its columns are prescribed and the other columns vary, are described. The characteristic polynomial of [A B] is defined as the largest determinantal divisor (or the product of the invariant factors) of [xI n - A - B]. This result generalizes a previous theorem by H. Wimmer which studies the same problem when t = 0. As a consequence, it is extended to arbitrary fields a result, already proved for infinite fields, that describes all the possible characteristic polynomials of a square matrix when an arbitrary submatrix is fixed and the other entries vary. Finally, applications to the stabilization and observability of linear systems by state feedback are studied.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 12