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The Relation Between the Companion Matrix and the Companion Polynomial in R-4 Algebras
We prove that the quaternionic companion polynomial is identical with the characteristic polynomial of the complex matrix which is obtained by isomorphism from the quaternionic companion matrix. And we show that th...
Applied mathematics
- 2018 •
- Jimp •
- Link
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
Výsledek na webu
Zero points of quadratic matrix polynomials
Our aim is to classify and compute zeros of the quadratic two sided matrix polynomials, i.e. quadratic polynomials whose matrix coefficients are located at both sides of the powers of the matrix variable. ...
BA - Obecná matematika
- 2013 •
- D
Rok uplatnění
D - Stať ve sborníku
On Chebyshev Polynomials of Matrices
The mth Chebyshev polynomial of a square matrix A is the monic polynomial that minimizes the matrix 2-norm of p(A) over all monic polynomials p(z) of degree m. This polynomial is uniquely defined ...
BA - Obecná matematika
- 2010 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Modular shift of a polynomial matrix using Matlab.
Efficient algorithm for modular shift of a polynomial matrix is proposed in this note.The algorithm avoids any iteration that is inherent in standard Euclidean algorithm for division of polynomial matrices.It assumes that t...
BC - Teorie a systémy řízení
- 2002 •
- D
Rok uplatnění
D - Stať ve sborníku
A Toeplitz Algorithm for Polynomial J-Spectral Factorization
of a para-Hermitian polynomial matrix. The input matrix can be singular or indefinite zerosof the input polynomial matrix are given as input data. The algorithm is based block Toeplitz matrices, polyn...
BC - Teorie a systémy řízení
- 2006 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Polynomial matrices, LMIs and static output feedback.
In the polynomial approach to systems control, the static output feedback problem can be formulated as follows: given two polynomial matrices D(s) and N(s), find a constant matrix K such that polynomial matrix<...
BC - Teorie a systémy řízení
- 2001 •
- D
Rok uplatnění
D - Stať ve sborníku
On Diagonalizable Quantum Weighted Hankel Matrices
A semi-infinite weighted Hawith the continuous q-Laguerre polynomials, is diagonalized. As an application, several new integral formulas for selected quantum orthogonal polynomials are deduced. In addition, an open research problem ...
Pure mathematics
- 2022 •
- C •
- Link
Rok uplatnění
C - Kapitola v odborné knize
Výsledek na webu
Proper feedback compensators for a strictly proper plant by polynominal equations
We study the polynomial matrix compensator equation X1Dr+Y1Nr = Dk (COMP), where (a) the right-coprime polynomial matrix pair (Nr,Dr) is given by the strictly proper rational plant right matrix-fraction P ...
BC - Teorie a systémy řízení
- 2005 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Implementation of polynomial algebra via spectra.
Polynomial methods are today an effective method for the synthesis of control systems. The calculation of certain function with polynomial matrices which are represented by coefficients of polynomials are time consuming. If...
BC - Teorie a systémy řízení
- 2002 •
- D
Rok uplatnění
D - Stať ve sborníku
Resolvent of matrix polynomials, pseudospectra and inversion problems.
This paper deals with the mathematical model of dynamical systems described by differential equations. The formulae for resolvents of matrix polynomials and for derivative resolvents are given and extension of the definition of pseu...
BI - Akustika a kmity
- 2002 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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