Results 11 to 20 of about 2,093 (267)
Algebraic linearizations of matrix polynomials
Linear Algebra and its Applications, 2019 We show how to construct linearizations of matrix polynomials $z\mathbf{a}(z)\mathbf{d}_0 + \mathbf{c}_0$, $\mathbf{a}(z)\mathbf{b}(z)$, $\mathbf{a}(z) + \mathbf{b}(z)$ (when $\mathrm{deg}\left(\mathbf{b}(z)\right) < \mathrm{deg}\left(\mathbf{a}(z)\right)$), and $z\mathbf{a}(z)\mathbf{d}_0\mathbf{b}(z) + \mathbf{c_0}$ from linearizations of the ...
Eunice Y.S. Chan +4 more
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Generalized Standard Triples for Algebraic Linearizations of Matrix Polynomials
The Electronic Journal of Linear Algebra, 2021 We define generalized standard triples $\boldsymbol{X}$, $\boldsymbol{Y}$, and $L(z) = z\boldsymbol{C}_{1} - \boldsymbol{C}_{0}$, where $L(z)$ is a linearization of a regular matrix polynomial $\boldsymbol{P}(z) \in \mathbb{C}^{n \times n}[z]$, in order to use the representation $\boldsymbol{X}(z \boldsymbol{C}_{1}~-~\boldsymbol{C}_{0})^{-1}\boldsymbol{
Eunice Y.S. Chan +2 more
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Point-evaluation functionals on algebras of symmetric functions on $(L_\infty)^2$
Karpatsʹkì Matematičnì Publìkacìï, 2019 It is known that every continuous symmetric (invariant under the composition of its argument with each Lebesgue measurable bijection of $[0,1]$ that preserve the Lebesgue measure of measurable sets) polynomial on the Cartesian power of the complex Banach
T.V. Vasylyshyn
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Axioms, 2023 In this paper we formulate necessary conditions for the stability of certain quadrature methods for Mellin type singular integral equations on an interval.
Peter Junghanns, Robert Kaiser
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Hilbert polynomials of the algebras of $SL_ 2$-invariants
Karpatsʹkì Matematičnì Publìkacìï, 2018 We consider one of the fundamental problems of classical invariant theory, the research of Hilbert polynomials for an algebra of invariants of Lie group $SL_2$.
N.B. Ilash
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ITM Web of Conferences, 2018 We review classical concepts of resultants of algebraic polynomials, and we adapt some of these concepts to objects in differential algebra, such as linear differential operators and differential polynomials.
McCallum Scott, Winkler Franz
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A linear algebra approach to the hybrid Sheffer–Appell polynomials [PDF]
Mathematical Sciences, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Khan, Subuhi, Ali, Mahvish
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A standard form in (some) free fields: How to construct minimal linear representations
Open Mathematics, 2020 We describe a standard form for the elements in the universal field of fractions of free associative algebras (over a commutative field). It is a special version of the normal form provided by Cohn and Reutenauer and enables the use of linear algebra ...
Schrempf Konrad
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Spectra of some algebras of entire functions of bounded type, generated by a sequence of polynomials
Karpatsʹkì Matematičnì Publìkacìï, 2019 In this work, we investigate the properties of the topological algebra of entire functions of bounded type, generated by a countable set of homogeneous polynomials on a complex Banach space. Let $X$ be a complex Banach space. We consider a subalgebra $
S.I. Halushchak
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On λ-linear functionals arising from p-adic integrals on Z p $\mathbb{Z}_{p}$
Advances in Difference Equations, 2021 The aim of this paper is to determine the λ-linear functionals sending any given polynomial p ( x ) $p(x)$ with coefficients in C p $\mathbb{C}_{p}$ to the p-adic invariant integral of P ( x ) $P(x)$ on Z p $\mathbb{Z}_{p}$ and also to that of P ( x 1 + ⋯
Dae San Kim +4 more
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