منابع مشابه
Ranks of Random Matrices and Graphs
OF THE DISSERTATION Ranks of Random Matrices and Graphs by Kevin Costello Dissertation Director: Van Vu Let Qn be a random symmetric matrix whose entries on and above the main diagonal are independent random variables (e.g. the adjacency matrix of an Erdős-Rényi random graph). In this thesis we study the behavior of the rank of the matrix in terms of the probability distribution of the entries....
متن کاملRanks and signatures of adjacency matrices
Two simple operations on graphs (deleting isolated vertices, and identifying vertices with the same neighbour sets) do not change the rank and signature of the adjacency matrix. Moreover, for any given rank, there are only finitely many reduced graphs (those in which distinct vertices have distinct neighbour sets) of any given rank. It follows that any graph parameter which is unchanged by the ...
متن کاملRanks of matrices with few distinct entries
An L-matrix is a matrix whose off-diagonal entries belong to a set L, and whose diagonal is zero. Let N(r, L) be the maximum size of a square L-matrix of rank at most r. Many applications of linear algebra in extremal combinatorics involve a bound on N(r, L). We review some of these applications, and prove several new results on N(r, L). In particular, we classify the sets L for which N(r, L) i...
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We survey recent results on p-ranks of certain inclusion matrices arising from a finite projective space or a finite symplectic space. 2000 Mathematics Subject Classification: 05E20, 20G05, 20C33.
متن کاملRanks of Quotients, Remainders and $p$-Adic Digits of Matrices
For a prime p and a matrix A ∈ Zn×n, write A as A = p(A quo p)+ (A rem p) where the remainder and quotient operations are applied element-wise. Write the p-adic expansion of A as A = A[0] + pA[1] + p2A[2] + · · · where each A[i] ∈ Zn×n has entries between [0, p − 1]. Upper bounds are proven for the Z-ranks of A rem p, and A quo p. Also, upper bounds are proven for the Z/pZ-rank of A[i] for all ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1993
ISSN: 0024-3795
DOI: 10.1016/0024-3795(93)90324-h