scholarly journals Some Results on the Hermite Matrix

2019 ◽  
Vol 7 (1) ◽  
Keyword(s):  
Hermite Matrix

scholarly journals On Hermite-Hermite matrix polynomials

2008 ◽  
Vol 133 (4) ◽  
pp. 421-434 ◽  
Author(s):  
M. S. Metwally ◽  
M. T. Mohamed ◽  
A. Shehata
Keyword(s):  
Matrix Polynomials ◽  
Hermite Matrix

scholarly journals Determinantal representations and the Hermite matrix

2013 ◽  
Vol 62 (2) ◽  
pp. 407-420 ◽  
Author(s):  
Tim Netzer ◽  
Daniel Plaumann ◽  
Andreas Thom
Keyword(s):  
Hermite Matrix

scholarly journals Q-matrix polynomials in several variables

Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 2059-2067 ◽  
Author(s):  
Bayram Çekim
Keyword(s):  
Matrix Functions ◽  
Matrix Polynomials ◽  
Several Variables ◽  
Generating Matrix Functions ◽  
Hermite Matrix ◽  
Q Matrix ◽  
Generating Matrix

In the present paper, we define q-matrix polynomials in several variables which reduces Chan-Chyan-Srivastava and Lagrange-Hermite matrix polynomials in [6]. Then several results involving generating matrix functions for these matrix polynomials are derived.

scholarly journals On generalized two-index Hermite matrix polynomials

2017 ◽  
Vol 18 (1) ◽  
pp. 223 ◽  
Author(s):  
Levent Kargin ◽  
Veli Kurt
Keyword(s):  
Matrix Polynomials ◽  
Hermite Matrix

scholarly journals On new extensions of the generalized Hermite matrix polynomials

2019 ◽  
Vol 22 (2) ◽  
pp. 203-222
Author(s):  
Ayman Shehata
Keyword(s):  
Integral Representations ◽  
Matrix Functions ◽  
Matrix Polynomials ◽  
Summation Formulae ◽  
Summation Formulas ◽  
Fractional Calculus Operators ◽  
Generating Matrix Functions ◽  
Hermite Matrix ◽  
Generating Matrix ◽  
Matrix Recurrence Relations

Various families of generating matrix functions have been established in diverse ways. The objective of the present paper is to investigate these generalized Hermite matrix polynomials, and derive some important results for them, such as, the generating matrix functions, matrix recurrence relations, an expansion of xnI, finite summation formulas, addition theorems, integral representations, fractional calculus operators, and certain other implicit summation formulae.

scholarly journals From linear algebra to quantum information

2021 ◽  
pp. 032-047
Author(s):  
Yu LW ◽  
Wang NL ◽  
Kanemitsu S
Keyword(s):  
Functional Analysis ◽  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Information ◽  
Linear Algebra ◽  
Smooth Transition ◽  
Quantum Computers ◽  
Hermite Operator ◽  
Hermite Matrix ◽  
Hermite Operators

Anticipating the realization of quantum computers, we propose the most reader-friendly exposition of quantum information and qubits theory. Although the latter lies within framework of linear algebra, it has some fl avor of quantum mechanics and it would be easier to get used to special symbols and terminologies. Quantum mechanics is described in the language of functional analysis: the state space (the totality of all states) of a quantum system is a Hilbert space over the complex numbers and all mechanical quantities are taken as Hermite operators. Hence some basics of functional analysis is necessary. We make a smooth transition from linear algebra to functional analysis by comparing the elements in these theories: Hilbert space vs. fi nite dimensional vector space, Hermite operator vs. linear map given by a Hermite matrix. Then from Newtonian mechanics to quantum mechanics and then to the theory of qubits. We elucidate qubits theory a bit by accommodating it into linear algebra framework under these precursors.

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