We introduce a class of structure matrices called transpose complemental' structure matrices. We give a characterization of the n-extendable transpose complementary structure matrices with trace k, where k = 0, 2. We 'also prove that a nonsingular matrix and its inverse have the same S-rank lbr this
On the matrices of given rank in a large subspace
✍ Scribed by Clément de Seguins Pazzis
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 177 KB
- Volume
- 435
- Category
- Article
- ISSN
- 0024-3795
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📜 SIMILAR VOLUMES
For a simple graph G on n vertices, the minimum rank of G over a field F, written as mr F (G), is defined to be the smallest possible rank among all n × n symmetric matrices over F whose (i, j)th entry (for i / = j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. A symmetric integ
## Abstract Let __λ__ be an eigenvalue of an infinite Toeplitz band matrix __A__ and let __λ~n~__ be an eigenvalue of the __n__ ×__n__ truncation __A~n~__ of __A__ . Suppose __λ~n~__ converges to __λ__ as __n__ → ∞. We show that generically the eigenspaces for __λ~n~__ are onedimensional and contai