منابع مشابه
Combinatorial Eigenvalues of Matrices
Let S be a subset of diagonal entries of an n × n complex matrix A. When the members of S have a common value which is equal to an eigenvalue of A, then S is a critical diagonal set of A. The existence of such a set is equivalent to the matrix Ã, obtained from A by setting its diagonal entries equal to zero, having an s × t zero submatrix with s + t ≥ n + 1. If S is a minimal critical diagonal ...
متن کاملOn the eigenvalues of some matrices based on vertex degree
The aim of this paper is to compute some bounds of forgotten index and then we present spectral properties of this index. In continuing, we define a new version of energy namely ISI energy corresponded to the ISI index and then we determine some bounds for it.
متن کاملEigenvalues and Pseudo-eigenvalues of Toeplitz Matrices
The eigenvalues of a nonhermitian Toeplitz matrix A are usually highly sensitive to perturbations, having condition numbers that increase exponentially with the dimension N. An equivalent statement is that the resolvent ( ZZ A)’ of a Toeplitz matrix may be much larger in norm than the eigenvalues alone would suggest-exponentially large as a function of N, even when z is far from the spectrum. B...
متن کاملthe second immanant of some combinatorial matrices
let $a = (a_{i,j})_{1 leq i,j leq n}$ be an $n times n$ matrixwhere $n geq 2$. let $dt(a)$, its second immanant be the immanant corresponding to the partition $lambda_2 = 2,1^{n-2}$. let $g$ be a connected graph with blocks $b_1, b_2, ldots b_p$ and with$q$-exponential distance matrix $ed_g$. we given an explicitformula for $dt(ed_g)$ which shows that $dt(ed_g)$ is independent of the manner in ...
متن کاملEigenvalues in Combinatorial Optimization ∗
In the last decade many important applications of eigenvalues and eigenvectors of graphs in combinatorial optimization were discovered. The number and importance of these results is so fascinating that it makes sense to present this survey. ∗This article appeared in Combinatorial and Graph-Theoretical Problems in Linear Algebra, R. A. Brualdi, S. Friedland, V. Klee, Eds., IMA Volumes in Mathema...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1992
ISSN: 0024-3795
DOI: 10.1016/0024-3795(92)90310-7