Boolean rank of upset tournament matrices

نویسندگان
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Boolean Matrices . . . Neither Boolean nor Matrices

Boolean matrices, the incidence matrices of a graph, are known not to be the (universal) matrices of a Boolean algebra. Here, we also show that their usual composition cannot make them the matrices of any algebra. Yet, later on, we “show” that it can. This seeming paradox comes from the hidden intrusion of a widespread set-theoretical (mis) definition and notation and denies its harmlessness. A...

متن کامل

On 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...

متن کامل

Local Out-Tournaments with Upset Tournament Strong Components I: Full and Equal {0, 1}-Matrix Ranks

A digraph D is a local out-tournament if the outset of every vertex: is a tournament. Here, we use local out-tournaments, whose strong components are upset tournaments, to explore the corresponding ranks of the adjacency matrices. Of specific interest is the out-tournament whose adjacency matrix has boolean, nonnegative integer, term, and real rank all equal to the number of vertices, n. Corres...

متن کامل

Ela Even and Odd Tournament Matrices with Minimum Rank over Finite Fields

The (0, 1)-matrix A of order n is a tournament matrix provided A + A + I = J, where I is the identity matrix, and J = Jn is the all 1’s matrix of order n. It was shown by de Caen and Michael that the rank of a tournament matrix A of order n over a field of characteristic p satisfies rankp(A) ≥ (n − 1)/2 with equality if and only if n is odd and AA = O. This article shows that the rank of a tour...

متن کامل

Ela Singular Values of Tournament Matrices

Upper and lower bounds on both the largest and smallest singular values of a tournament matrix M of order n are obtained. For most values of n, the matrices M for which equality holds are characterized.

متن کامل

ذخیره 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: 2012

ISSN: 0024-3795

DOI: 10.1016/j.laa.2011.11.003