Minimization problems for (R,S)-symmetric and (R,S)-skew symmetric matrices
نویسندگان
چکیده
منابع مشابه
Principally Unimodular Skew-Symmetric Matrices
A square matrix is principally unimodular if every principal submatrix has determinant 0 or 1. Let A be a symmetric (0; 1)-matrix, with a zero diagonal. A PU-orientation of A is a skew-symmetric signing of A that is PU. If A 0 is a PU-orientation of A, then, by a certain decomposition of A, we can construct every PU-orientation of A from A 0. This construction is based on the fact that the PU-o...
متن کاملCommutators of Skew-Symmetric Matrices
In this paper we develop a theory for analysing the size of a Lie bracket or commutator in a matrix Lie algebra. Complete details are given for the Lie algebra so(n) of skew symmetric matrices. 1 Norms and commutators in Mn[R] and so(n) This paper is concerned with the following question. Let g be a Lie algebra (Carter, Segal & Macdonald 1995, Humphreys 1978, Varadarajan 1984). Given X,Y ∈ g an...
متن کاملOn skew-symmetric differentiation matrices
The theme of this paper is the construction of finite-difference approximations to the first derivative in the presence of Dirichlet boundary conditions. Stable implementation of splitting-based discretisation methods for the convectiondiffusion equation requires the underlying matrix to be skew symmetric and this turns out to be a surprisingly restrictive condition. We prove that no skewsymmet...
متن کاملA Penalty Method for Rank Minimization Problems in Symmetric Matrices∗
The problem of minimizing the rank of a symmetric positive semidefinite matrix subject to constraints can be cast equivalently as a semidefinite program with complementarity constraints (SDCMPCC). The formulation requires two positive semidefinite matrices to be complementary. We investigate calmness of locally optimal solutions to the SDCMPCC formulation and hence show that any locally optimal...
متن کاملUnitary Completions Of Complex Symmetric And Skew Symmetric Matrices ∗
Unitary symmetric completions of complex symmetric matrices are obtained via Autonne decomposition. The problem arises from atomic physics. Of independent interest unitary skew symmetric completions of skew symmetric matrices are also obtained by Hua decomposition.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2004
ISSN: 0024-3795
DOI: 10.1016/j.laa.2004.03.035