Ela on Determining Minimal Spectrally
نویسندگان
چکیده
A new family of minimal spectrally arbitrary patterns is presented which allow for arbitrary spectrum by using the Nilpotent-Jacobian method introduced in [J.H. Drew, C.R. Johnson, D.D. Olesky, and P. van den Driessche. Spectrally arbitrary patterns.Lin. Alg. and Appl. 308:121137, 2000]. The novel approach here is the use of the Intermediate Value Theorem to avoid finding an explicit nilpotent realization of the new minimal spectrally arbitrary patterns.
منابع مشابه
Ela Spectrally
An n × n complex sign pattern matrix S is said to be spectrally arbitrary if for every monic nth degree polynomial f(λ) with coefficients from C, there is a complex matrix in the complex sign pattern class of S such that its characteristic polynomial is f(λ). If S is a spectrally arbitrary complex sign pattern matrix, and no proper subpattern of S is spectrally arbitrary, then S is a minimal sp...
متن کاملar X iv : m at h / 05 08 20 7 v 1 [ m at h . R A ] 1 1 A ug 2 00 5 ON DETERMINING MINIMAL SPECTRALLY ARBITRARY PATTERNS
In this paper we present a new family of minimal spectrally arbitrary patterns which allow for arbitrary spectrum by using the Nilpotent-Jacobian method introduced in [3]. The novel approach here is that we use the Intermediate Value Theorem to avoid finding an explicit nilpotent realization of the new minimal spectrally arbitrary patterns.
متن کاملOn determining minimal spectrally arbitrary patterns
A new family of minimal spectrally arbitrary patterns is presented which allow for arbitrary spectrum by using the Nilpotent-Jacobian method introduced in [J.H. Drew, C.R. Johnson, D.D. Olesky, and P. van den Driessche. Spectrally arbitrary patterns.Lin. Alg. and Appl. 308:121137, 2000]. The novel approach here is the use of the Intermediate Value Theorem to avoid finding an explicit nilpotent ...
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An n × n sign pattern matrix A is an inertially arbitrary pattern if for every nonnegative triple (n1, n2, n3) with n1 + n2 + n3 = n, there is a real matrix in the sign pattern class of A having inertia (n1, n2, n3). An n× n sign pattern matrix A is a spectrally arbitrary pattern if for any given real monic polynomial r(x) of degree n, there is a real matrix in the sign pattern class of A with ...
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...
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