Inverse Closed Ray-nonsingular Cones of Matrices
نویسندگان
چکیده
A description is given of those ray-patterns, which will be called inverse closed ray-nonsingular, of complex matrices that contain invertible matrices only and are closed under inversion. Here, two n × n matrices are said to belong to the same ray-pattern if in each position either the entries of both matrices are zeros, or both entries are nonzero and their quotient is positive. Possible Jordan forms of matrices in the inverse closed ray-nonsingular ray-patterns are characterized.
منابع مشابه
A Theory for Valiant's Matchcircuits (Extended Abstract)
The computational function of a matchgate is represented by its character matrix. In this article, we show that all nonsingular character matrices are closed under matrix inverse operation, so that for every k, the nonsingular character matrices of k-bit matchgates form a group, extending the recent work of Cai and Choudhary [1] of the same result for the case of k = 2, and that the single and ...
متن کاملA Theory for Valiant’s Matchcircuits
The computational function of a matchgate is represented by its character matrix. In this article, we show that all nonsingular character matrices are closed under matrix inverse operation, so that for every k, the nonsingular character matrices of k-bit matchgates form a group, extending the recent work of Cai and Choudhary [1] of the same result for the case of k = 2, and that the single and ...
متن کاملMatrix inversion and digraphs: the one factor case
The novel concept of a cyclic sequence of a digraph that has precisely one factor is defined, and is used to characterize the entries of the inverse of a matrix with such a digraph. This leads to a characterization of a strongly sign-nonsingular matrix in terms of cyclic sequences. Nonsingular nearly reducible matrices are a well-known class of matrices having precisely one nonzero diagonal, an...
متن کاملThe infinity norm bound for the inverse of nonsingular diagonal dominant matrices
In this note, we bound the inverse of nonsingular diagonal dominant matrices under the infinity norm. This bound is always sharper than the one in [P.N. Shivakumar, et al., On two-sided bounds related to weakly diagonally dominant M-matrices with application to digital dynamics, SIAM J. Matrix Anal. Appl. 17 (2) (1996) 298–312]. c © 2008 Published by Elsevier Ltd
متن کاملEquivariant Cohomology in Algebraic Geometry Lecture Thirteen: Toric Varieties
Let X be a complete nonsingular toric variety. In this lecture, we will descibe H∗ TX. First we recall some basic notions about toric varieties. Let T be an n-dimensional torus with character group M , and let N = HomZ(M,Z) be the dual lattice. Then X = X(Σ), for a complete nonsingular fan Σ. That is, Σ is a collection of cones σ in NR = N ⊗ZR such that two cones meet along a face of each; each...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004