کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4603383 1336958 2008 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Products of two involutions with prescribed eigenvalues and some applications
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Products of two involutions with prescribed eigenvalues and some applications
چکیده انگلیسی

Let F be a field. In [Djokovic, Product of two involutions, Arch. Math. 18 (1967) 582–584] it was proved that a matrix A∈Fn×n can be written as A=BC, for some involutions B,C∈Fn×n, 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 charF≠2, we describe the possible similarity classes of (P11⊕P22)P-1, when the nonsingular matrix P=[Pij]∈Fn×n, i,j∈{1,2} and P11∈Fs×s, varies.When F is an algebraically closed field and charF≠2, we also describe the possible similarity classes of [Aij]∈Fn×n, i,j∈{1,2}, when A11 and A22 are square zero matrices and A12 and A21 vary.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 429, Issue 7, 1 October 2008, Pages 1663-1678