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
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
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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
Journal: Linear Algebra and its Applications - Volume 429, Issue 7, 1 October 2008, Pages 1663-1678