Products of two involutions with prescribed eigenvalues and some applications

• Type: Article in International Scientific Journal
• Date: 2008

Authors

Susana Borges Furtado (Author) FEP

Journal

Title: Linear Algebra and Its Applications

Vol. 429

Pages: 1663-1678

ISSN: 0024-3795

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 6 Citations

ISI Web of Science

Scopus - 6 Citations

Scientific classification

FOS: Natural sciences

Other information

Authenticus ID: P-003-VY8

DOI: 10.1016/j.laa.2008.04.044

Abstract (EN): Let F be a field. In [Djokovic, Product of two involutions, Arch. Math. 18 (1967) 582-584] it was proved that a matrix A epsilon F-nxn can be written as A = BC, for some involutions B, C epsilon F-nxn, if and only if A is similar to A(-1). In this paper we describe the possible eigenvalues of the matrices B and C. As a consequence, in case char F not equal 2, we describe the possible similarity classes of (P-11 circle times P-22) P-1, when the nonsingular matrix P = [P-ij] epsilon F-nxn, i, j epsilon {1, 2} and P-11 epsilon F-sxs, varies. When F is an algebraically closed field and char F not equal 2, we also describe the possible similarity classes of [A(ij)] epsilon F-nxn, i, j epsilon {1, 2}, when A(11) and A(22) are square zero matrices and A(12) and A(21) vary.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16