نتایج جستجو برای: rank 1 matrices
تعداد نتایج: 2859864 فیلتر نتایج به سال:
The principal permanent rank characteristic sequence is a binary sequence r0r1 · · · rn where rk = 1 if there exists a principal square submatrix of size k with nonzero permanent and rk = 0 otherwise, and r0 = 1 if there is a zero diagonal entry. A characterization is provided for all principal permanent rank sequences obtainable by the family of nonnegative matrices as well as the family of no...
The minimum rank of a simple graph G over a field F is the smallest possible rank among all symmetric matrices over F whose ijth entry (for i != j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. We define a universally optimal matrix to be an integer matrix A such that every off-diagonal entry of A is 0, 1, or −1, and for all fields F , the rank of A is the minimum rank over ...
In this paper we study a generalization of Kruskal’s permutation lemma to partitioned matrices. We define the k’-rank of partitioned matrices as a generalization of the k-rank of matrices. We derive a lower-bound on the k’-rank of Khatri–Rao products of partitioned matrices. We prove that Khatri–Rao products of partitioned matrices are generically full column rank.
In this thesis we are concerned with themes suggested by rank properties of subspaces of matrices. Historically, most work on these topics has been devoted to matrices over such fields as the real or complex numbers, where geometric or analytic methods may be applied. Such techniques are not obviously applicable to finite fields, and there were very few general theorems relating to rank problem...
A central question in random matrix theory is universality. When an emergent phenomena observed from a large collection of chosen variables it natural to ask if this behavior specific the variable or occurs for larger class variables. The rank statistics matrices uniformly $\operatorname{Mat}(\mathbf{F}_q)$ over finite field are well understood. The universality properties these not yet fully...
It is well known that the set of separable pure states is measure 0 in the set of pure states. We extend this fact and show that the set of rank r separable states is measure 0 in the set of rank r states provided r is less than ∏p i=1 ni + p − ∑ ni. Recently quite a few authors have looked at low rank separable and entangled states. (See [1] and the references therein and [2] and [3] Therefore...
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