The p-Rank of (0, 1)-matrices
نویسندگان
چکیده
منابع مشابه
(0, ±1) Ideal Matrices
A (0; 1) matrix A is said to be ideal if all the vertices of the polytope Q(A) = fx : Ax 1; 0 x 1g are integral. The issue of nding a satisfactory characterization of those matrices which are minimally non-ideal is a well known open problem. An outstanding result toward the solution of this problem, due to Alfred Lehman, is the description of crucial properties of minimally non-ideal matrices. ...
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Perfect graphs and perfect 0,l matrices are well studied in the literature. Here we introduce perfect 0, f 1 matrices. Our main result is a characterization of these matrices in terms of a family of perfect 0,l matrices. 0 Elsevim Science Inc., 1997 * This work was supported in part by NSF grants DMI-9424348 and DMS-9509581, and by ONR grant NOOO14-89-J-1063. LINEAR ALGEBRA AND ITS APPLZCATIONS...
متن کاملEla the Maximum Order of Reduced Square (0, 1)-matrices with a given Rank∗
The maximum order of a square (0, 1)-matrix A with a fixed rank r is considered, provided A has no repeated rows or columns. When A is the adjacency matrix of a graph, Kotlov and Lovász [A. Kotlov and L. Lovász. The rank and size of graphs. J. Graph Theory, 23:185–189, 1996.] proved that the maximum order equals Θ(2r/2). In this note, it is showed that this result remains correct if A is symmet...
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The energy of a matrix is the sum of its singular values. We study the energy of (0, 1)matrices and present two methods for constructing balanced incomplete block designs whose incidence matrices have the maximum possible energy amongst the family of all (0, 1)-matrices of given order and total number of ones. We also find a new upper bound for the energy of (p, q)-bipartite graphs. AMS Subject...
متن کاملOn higher rank numerical hulls of normal matrices
In this paper, some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated. A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given. Moreover, using the extreme points of the numerical range, the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$, where $A_1...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1992
ISSN: 0097-3165
DOI: 10.1016/0097-3165(92)90043-t