On the multiplicities of digraph eigenvalues
نویسندگان
چکیده
We show various upper bounds for the order of a digraph (or mixed graph) whose Hermitian adjacency matrix has an eigenspace prescribed codimension. In particular, this generalizes so-called absolute bound (simple) graphs first shown by Delsarte, Goethals, and Seidel (1977) extended Bell Rowlinson (2003). doing so, we also adapt Blokhuis' theory (1983) harmonic analysis in real hyperbolic spaces to that complex spaces.
منابع مشابه
Eigenvalues, Multiplicities and Graphs
For a given graph, there is a natural question of the possible lists of multiplicities for the eigenvalues among the spectra of Hermitian matrices with that graph (no constraint is placed upon the diagonal entries of the matrices by the graph). Here, we survey some of what is known about this question and include some new information about it. There is a natural focus upon the case in which the...
متن کاملSharp Bounds for Eigenvalues and Multiplicities on Surfaces of Revolution
For surfaces of revolution diffeomorphic to S, it is proved that (S, can) provides sharp upper bounds for the multiplicities of all of the distinct eigenvalues. We also find sharp upper bounds for all the distinct eigenvalues and show that an infinite sequence of these eigenvalues are bounded above by those of (S, can). An example of such bounds for a metric with some negative curvature is pres...
متن کاملMultiplicities of the Eigenvalues of Periodic Dirac Operators
Let us consider the Dirac operator L = iJ d dx + U, J = ( 1 0 0 −1 ) , U = ( 0 a cos 2πx a cos 2πx 0 ) , where a 6= 0 is real, on I = [0, 1] with boundary conditions bc = Per, i.e., F (1) = F (0), and bc = Per−, i.e., F (1) = −F (0), F = ( f1 f2 ) ∈ H(I). Then σ(Lbc) = −σ(Lbc), and all λ ∈ σPer+(L(U)) are of multiplicity 2, while λ ∈ σPer−(L(U)) are simple (Thm 15). This is an analogue of E. L....
متن کاملsurvey on the rule of the due & hindering relying on the sheikh ansaris ideas
قاعده مقتضی و مانع در متون فقهی کم و بیش مستند احکام قرار گرفته و مورد مناقشه فقهاء و اصولیین می باشد و مشهور معتقند مقتضی و مانع، قاعده نیست بلکه یکی از مسائل ذیل استصحاب است لذا نگارنده بر آن شد تا پیرامون این قاعده پژوهش جامعی انجام دهد. به عقیده ما مقتضی دارای حیثیت مستقلی است و هر گاه می گوییم مقتضی احراز شد یعنی با ماهیت مستقل خودش محرز گشته و قطعا اقتضاء خود را خواهد داشت مانند نکاح که ...
15 صفحه اولDetermination of spurious eigenvalues and multiplicities of true eigenvalues using the real-part dual BEM
The complex-valued dual BEM has been employed by Chen and Chen (1998) to solve the acoustic modes of a cavity with or without a thin partition. A novel method using only the real part of the complex-valued dual BEM was found by Chen (1998) to be equivalent to the dual MRM. However, spurious eigenvalues occur. In this paper, we propose the singular value decomposition technique to ®lter out spur...
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: Linear Algebra and its Applications
سال: 2023
ISSN: ['1873-1856', '0024-3795']
DOI: https://doi.org/10.1016/j.laa.2023.04.008