Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598928 | Linear Algebra and its Applications | 2015 | 10 Pages |
Abstract
Fix a field K , a subset P⊆{1,…,k}×{1,…,m}P⊆{1,…,k}×{1,…,m} and an integer δ≤min{k,m}δ≤min{k,m}. Let C(m,k,P,K)C(m,k,P,K) be the vector space of all k×mk×m matrices with entries ai,j=0ai,j=0 if (i,j)∉P(i,j)∉P. Let α(δ,K)α(δ,K) be the maximal dimension of a linear subspace V⊆C(m,k,P,K)V⊆C(m,k,P,K) such that all A∈V∖{0}A∈V∖{0} have rank ≥δ . We show that known lower bounds for α(δ,K)α(δ,K), for K one (resp. several, resp. almost all) finite field give the same lower bounds for some (resp. many, resp. all) number fields.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
E. Ballico,