Polynomials and Numerical Ranges
نویسندگان
چکیده
منابع مشابه
Higher numerical ranges of matrix polynomials
Let $P(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. In this paper, some algebraic and geometrical properties of the $k$-numerical range of $P(lambda)$ are investigated. In particular, the relationship between the $k$-numerical range of $P(lambda)$ and the $k$-numerical range of its companion linearization is stated. Moreover, the $k$-numerical...
متن کاملGeneralized numerical ranges of matrix polynomials
In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.
متن کاملHigher rank numerical ranges of rectangular matrix polynomials
In this paper, the notion of rank-k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for ϵ > 0; the notion of Birkhoff-James approximate orthogonality sets for ϵ-higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed denitions yield a natural genera...
متن کاملhigher numerical ranges of matrix polynomials
let $p(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. in this paper, some algebraic and geometrical properties of the $k$-numerical range of $p(lambda)$ are investigated. in particular, the relationship between the $k$-numerical range of $p(lambda)$ and the $k$-numerical range of its companion linearization is stated. moreover, the $k$-numerical ...
متن کاملgeneralized numerical ranges of matrix polynomials
in this paper, we introduce the notions of c-numerical range and c-spectrum of matrix polynomials. some algebraic and geometrical properties are investigated. we also study the relationship between the c-numerical range of a matrix polynomial and the joint c-numerical range of its coefficients.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1988
ISSN: 0002-9939
DOI: 10.2307/2046981