منابع مشابه
Ela Graphs Whose Minimal Rank Is Two
Let F be a field, G = (V, E) be an undirected graph on n vertices, and let S(F, G) be the set of all symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. For example, if G is a path, S(F, G) consists of the symmetric irreducible tridiagonal matrices. Let mr(F, G) be the minimum rank over all matrices in S(F, G). Then mr(F, G...
متن کاملGraphs whose minimal rank is two
Let F be a field, G = (V, E) be an undirected graph on n vertices, and let S(F,G) be the set of all symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. For example, if G is a path, S(F,G) consists of the symmetric irreducible tridiagonal matrices. Let mr(F,G) be the minimum rank over all matrices in S(F,G). Then mr(F,G) = 1...
متن کاملGraphs whose minimal rank is two: The finite fields case
Let F be a finite field, G = (V, E) be an undirected graph on n vertices, and let S(F,G) be the set of all symmetric n× n matrices over F whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let mr(F,G) be the minimum rank of all matrices in S(F,G). If F is a finite field with pt elements, p = 2, it is shown that mr(F,G) ≤ 2 if and only if the compl...
متن کاملEla Graphs Whose Minimal Rank Is Two: the Finite Fields Case∗
Let F be a finite field, G = (V, E) be an undirected graph on n vertices, and let S(F,G) be the set of all symmetric n× n matrices over F whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let mr(F,G) be the minimum rank of all matrices in S(F,G). If F is a finite field with pt elements, p = 2, it is shown that mr(F,G) ≤ 2 if and only if the compl...
متن کاملRank-two Graphs Whose C∗-algebras Are Direct Limits of Circle Algebras
We describe a class of rank-2 graphs whose C∗-algebras are AT algebras. For a subclass which we call rank-2 Bratteli diagrams, we compute the K-theory of the C∗-algebra. We identify rank-2 Bratteli diagrams whose C∗-algebras are simple and have real-rank zero, and characterise the K-invariants achieved by such algebras. We give examples of rank-2 Bratteli diagrams whose C∗-algebras contain as f...
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ژورنال
عنوان ژورنال: The Electronic Journal of Linear Algebra
سال: 2004
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1137