Decompositions of minimum rank matrices
نویسندگان
چکیده
منابع مشابه
On generalized Hadamard matrices of minimum rank
Generalized Hadamard matrices of order qn−1 (q a prime power, n ≥ 2) over GF (q) are related to symmetric nets in affine 2-(qn, qn−1, (qn−1 − 1)/(q − 1)) designs invariant under an elementary abelian group of order q acting semi-regularly on points and blocks. The rank of any such matrix over GF (q) is greater than or equal to n− 1. It is proved that a matrix of minimum q-rank is unique up to a...
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Let F be a field, let G be a simple graph on n vertices, and let S (G) be the class of all F -valued symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. For each graph G, there is an associated minimum rank class, M R (G) consisting of all matrices A ∈ S (G) with rankA = mr (G), the minimum rank among all matrices in S (G)....
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Let F be a field, let G be a simple graph on n vertices, and let S (G) be the class of all F -valued symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. For each graph G, there is an associated minimum rank class, M R (G) consisting of all matrices A ∈ S (G) with rankA = mr (G), the minimum rank among all matrices in S (G)....
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2013
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.12.036