An Eigenvalue Inclusion Set for Matrices with a Constant Main Diagonal Entry
نویسندگان
چکیده
منابع مشابه
Regular symmetric Hadamard matrices with constant diagonal
We survey constructions of regular symmetric Hadamard matrices with constant diagonal, and point out some errors in the literature.
متن کاملDiagonal entry restrictions in minimum rank matrices
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)....
متن کاملEla Diagonal Entry Restrictions in Minimum Rank Matrices
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)....
متن کاملA Note on the Ranks of Set-Inclusion Matrices
A recurrence relation is derived for the rank (over most fields) of the set-inclusion matrices on a finite ground set. Given a finite set X of say v elements, let W = Wt,k(v) be the (0,1)-matrix of inclusions for t-subsets versus k-subsets of X : WT,K = 1 if T is contained in K, and 0 otherwise. These matrices play a significant part in several combinatorial investigations, see e.g. ([2], Thm. ...
متن کاملEla a Contribution to Collatz’s Eigenvalue Inclusion Theorem for Nonnegative Irreducible Matrices∗
The matrix calculus is widely applied in various branches of mathematics and control system engineering. In this paper properties of real matrices with nonnegative elements are studied. The classical Collatz theorem is unique and immediately applicable to estimating the spectral radius of nonnegative irreducible matrices. The coherence property is identified. Then the Perron–Frobenius theorem a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Symmetry
سال: 2018
ISSN: 2073-8994
DOI: 10.3390/sym10120745