Matrix description of multivariable polynomials
نویسندگان
چکیده
منابع مشابه
Multivariable Construction of Extended Jacobi Matrix Polynomials
The main aim of this paper is to construct a multivariable extension with the help of the extended Jacobi matrix polynomials (EJMPs). Generating matrix functions and recurrence relations satisfied by these multivariable matrix polynomials are derived. Furthermore, general families of multilinear and multilateral generating matrix functions are obtained and their applications are presented.
متن کاملThe Matrix Version for the Multivariable Humbert Polynomials
In this paper, the matrix extension of the multivariable Humbert polynomials is introduced. Various families of linear, multilinear and multilateral generating matrix functions of these matrix polynomials are presented. Miscellaneous applications are also discussed. 2000 Mathematics Subject Classification: 33C25; 15A60
متن کاملSquarefree Values of Multivariable Polynomials
Given f ∈ Z[x1, . . . , xn], we compute the density of x ∈ Z such that f(x) is squarefree, assuming the abc conjecture. Given f, g ∈ Z[x1, . . . , xn], we compute unconditionally the density of x ∈ Z such that gcd(f(x), g(x)) = 1. Function field analogues of both results are proved unconditionally. Finally, assuming the abc conjecture, given f ∈ Z[x], we estimate the size of the image of f({1, ...
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.
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: 1996
ISSN: 0024-3795
DOI: 10.1016/0024-3795(95)00104-2