کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4603548 1336964 2008 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Matrices with orthogonal groups admitting only determinant one
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Matrices with orthogonal groups admitting only determinant one
چکیده انگلیسی

The K-Orthogonal group of an n-by-n matrix K is defined as the set of nonsingular n-by-n matrices A satisfying ATKA=K, where the superscript T denotes transposition. These form a group under matrix multiplication. It is well-known that if K is skew-symmetric and nonsingular the determinant of every element of the K-Orthogonal group is +1, i.e., the determinant of any symplectic matrix is +1. We present necessary and sufficient conditions on a real or complex matrix K so that all elements of the K-Orthogonal group have determinant +1. These necessary and sufficient conditions can be simply stated in terms of the symmetric and skew-symmetric parts of K, denoted by Ks and Kw respectively, as follows: the determinant of every element in the K-Orthogonal group is +1 if and only if the matrix pencil Kw-λKs is regular and the matrix (Kw-λ0Ks)-1Kw has no Jordan blocks associated to the zero eigenvalue with odd dimension, where λ0 is any number such that det(Kw-λ0Ks)≠0.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 428, Issue 4, 1 February 2008, Pages 796-813