Matrices A such that AA+ - A+A are nonsingular
نویسندگان
چکیده
In this paper we study the class of square matrices A such that AA − AA is nonsingular, where A stands for the Moore–Penrose inverse of A. Among several characterizations we prove that for a matrix A of order n, the difference AA−AA is nonsingular if and only if R(A) ⊕ R(A) = Cn,1, where R(·) denotes the range space. Also we study matrices A such that R(A) = R(A).
منابع مشابه
Computation of the q-th roots of circulant matrices
In this paper, we investigate the reduced form of circulant matrices and we show that the problem of computing the q-th roots of a nonsingular circulant matrix A can be reduced to that of computing the q-th roots of two half size matrices B - C and B + C.
متن کاملSingular-value-like decomposition for complex matrix triples
The classical singular value decomposition for a matrix A ∈ Cm×n is a canonical form for A that also displays the eigenvalues of the Hermitian matrices AA∗ and A∗A. In this paper, we develop a corresponding decomposition for A that provides the Jordan canonical forms for the complex symmetric matrices AA and AA. More generally, we consider the matrix triple (A,G, Ĝ), where G ∈ Cm×m, Ĝ ∈ Cn×n ar...
متن کاملGlobal Stabilization of Attitude Dynamics: SDRE-based Control Laws
The State-Dependant Riccati Equation method has been frequently used to design suboptimal controllers applied to nonlinear dynamic systems. Different methods for local stability analysis of SDRE controlled systems of order greater than two such as the attitude dynamics of a general rigid body have been extended in literature; however, it is still difficult to show global stability properties of...
متن کاملEssentially Retractable Modules
We call a module essentially retractable if HomR for all essential submodules N of M. For a right FBN ring R, it is shown that: (i) A non-zero module is retractable (in the sense that HomR for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii) A non-zero module is essentially retractable if and on...
متن کاملCongruence of Hermitian Matrices by Hermitian Matrices
Two Hermitian matrices A, B ∈ Mn(C) are said to be Hermitian-congruent if there exists a nonsingular Hermitian matrix C ∈ Mn(C) such that B = CAC. In this paper, we give necessary and sufficient conditions for two nonsingular simultaneously unitarily diagonalizable Hermitian matrices A and B to be Hermitian-congruent. Moreover, when A and B are Hermitian-congruent, we describe the possible iner...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Applied Mathematics and Computation
دوره 217 شماره
صفحات -
تاریخ انتشار 2010