منابع مشابه
Spectrally Arbitrary Ray Patterns
An n n ray pattern A is said to be spectrally arbitrary if for every monic n-th degree polynomial f(x) with coe¢ cients from C, there is a matrix in the pattern class of A such that its characteristic polynomial is f(x). In this article the authors develop a nilpotent-Jacobi method for establishing that an irreducible ray pattern and all its superpatterns are spectrally arbitrary. They use this...
متن کاملSparse spectrally arbitrary patterns
We explore combinatorial matrix patterns of order n for which some matrix entries are necessarily nonzero, some entries are zero, and some are arbitrary. In particular, we are interested in when the pattern allows any monic characteristic polynomial with real coefficients, that is, when the pattern is spectrally arbitrary. We describe some order n patterns that are spectrally arbitrary. We show...
متن کاملSpectrally arbitrary star sign patterns !
An n × n sign pattern Sn is spectrally arbitrary if, for any given real monic polynomial g(x) of degree n, there is a real matrix having sign pattern Sn and characteristic polynomial g(x). All n × n star sign patterns that are spectrally arbitrary, and all minimal such patterns, are characterized. This subsequently leads to an explicit characterization of all n × n star sign patterns that are p...
متن کاملMinimal Spectrally Arbitrary Sign Patterns
An n × n sign pattern A is spectrally arbitrary if given any self-conjugate spectrum there exists a matrix realization of A with that spectrum. If replacing any nonzero entry (or entries) of A by zero destroys this property, then A is a minimal spectrally arbitrary sign pattern. For n ≥ 3, several families of n × n spectrally arbitrary sign patterns are presented, and their minimal spectrally a...
متن کاملNilpotent matrices and spectrally arbitrary sign patterns
It is shown that all potentially nilpotent full sign patterns are spectrally arbitrary. A related result for sign patterns all of whose zeros lie on the main diagonal is also given.
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: 2000
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(00)00026-4