scholarly journals Universal Properties of Infinite Matrices

1996 ◽  
Vol 180 (2) ◽  
pp. 402-411 ◽  
Author(s):  
Roy O. Davies ◽  
Michael P. Drazin ◽  
Mark L. Roberts
Keyword(s):  
Infinite Matrices ◽  
Universal Properties

On a symbolic algebra for Hencky-Prandtl nets

1983 ◽  
Vol 94 (2) ◽  
pp. 341-350
Author(s):  
R. Hill
Keyword(s):  
General Solution ◽  
Boundary Value Problems ◽  
Classical Theory ◽  
Systematic Approach ◽  
Standard Technique ◽  
Field Equations ◽  
Infinite Matrices ◽  
Symbolic Algebra ◽  
Series Representations ◽  
Plane Deformations

AbstractIn the classical theory of plane deformations in isotropic plastic media, the field equations are hyperbolic and the orthogonal families of characteristics are known as Hencky-Prandtl nets. Their distinctive geometry has been given symbolic expression by Collins (1968), in an algebra of infinite matrices associated with canonical series representations of the general solution. This has become the standard technique when investigating boundary-value problems, both analytically and numerically. The basic framework of the algebra is here reorganized and developed. A systematic approach then leads to new identities which are shown to be fundamental in the algebraic hierarchy.

scholarly journals Fine Spectra of Tridiagonal Symmetric Matrices

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Muhammed Altun
Keyword(s):  
Explicit Form ◽  
Resolvent Operator ◽  
Sequence Spaces ◽  
Symmetric Matrices ◽  
Infinite Matrices ◽  
Banded Matrices ◽  
Lower Triangular ◽  
The Resolvent Operator

The fine spectra of upper and lower triangular banded matrices were examined by several authors. Here we determine the fine spectra of tridiagonal symmetric infinite matrices and also give the explicit form of the resolvent operator for the sequence spaces , , , and .

scholarly journals Representation of doubly infinite matrices as non-commutative Laurent series

2017 ◽  
Vol 5 (1) ◽  
pp. 250-257 ◽  
Author(s):  
María Ivonne Arenas-Herrera ◽  
Luis Verde-Star
Keyword(s):  
Laurent Series ◽  
Infinite Matrices ◽  
General Properties ◽  
Hessenberg Matrices ◽  
Diagonal Representation

Abstract We present a new way to deal with doubly infinite lower Hessenberg matrices based on the representation of the matrices as the sum of their diagonal submatrices. We show that such representation is a simple and useful tool for computation purposes and also to obtain general properties of the matrices related with inversion, similarity, commutativity, and Pincherle derivatives. The diagonal representation allows us to consider the ring of doubly infinite lower Hessenberg matrices over a ring R as a ring of Laurent series in one indeterminate, with coefficients in the ring of R-valued sequences that don’t commute with the indeterminate.

Infinite Matrices

2020 ◽  
pp. 71-88
Author(s):  
Mohammad Mursaleen ◽  
Feyzi Başar
Keyword(s):  
Infinite Matrices

scholarly journals Description of unitary representations of the group of infinite 𝑝-adic integer matrices

2021 ◽  
Vol 25 (21) ◽  
pp. 606-643
Author(s):  
Yury Neretin
Keyword(s):  
Irreducible Representation ◽  
Unitary Representations ◽  
Irreducible Representations ◽  
Infinite Matrices ◽  
Natural Topology ◽  
Content Type ◽  
Residue Ring ◽  
Finite Dimensional ◽  
Irreducible Unitary Representations

We classify irreducible unitary representations of the group of all infinite matrices over a p p -adic field ( p ≠ 2 p\ne 2 ) with integer elements equipped with a natural topology. Any irreducible representation passes through a group G L GL of infinite matrices over a residue ring modulo p k p^k . Irreducible representations of the latter group are induced from finite-dimensional representations of certain open subgroups.

scholarly journals Inversion of Bilateral Basic Hypergeometric Series

10.37236/1703 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Michael Schlosser
Keyword(s):  
Hypergeometric Series ◽  
Basic Hypergeometric Series ◽  
Matrix Inversion ◽  
Infinite Matrices ◽  
Inversion Result ◽  
Matrix Inverse ◽  
Bilateral Basic Hypergeometric Series ◽  
Summation Theorem ◽  
Lower Triangular

We present a new matrix inverse with applications in the theory of bilateral basic hypergeometric series. Our matrix inversion result is directly extracted from an instance of Bailey's very-well-poised ${}_6\psi_6$ summation theorem, and involves two infinite matrices which are not lower-triangular. We combine our bilateral matrix inverse with known basic hypergeometric summation theorems to derive, via inverse relations, several new identities for bilateral basic hypergeometric series.

scholarly journals The αAB-, βAB-, γab- and NAB-duals for sequence spaces

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6219-6231
Author(s):  
D. Foroutannia ◽  
H. Roopaei
Keyword(s):  
Sequence Spaces ◽  
The Other ◽  
Infinite Matrices ◽  
Multiplier Space

Let A = (an,k) and B = (bn,k) be two infinite matrices with real entries. The main purpose of this paper is to generalize the multiplier space for introducing the concepts of ?AB-, ?AB-, ?AB-duals and NAB-duals. Moreover, these duals are investigated for the sequence spaces X and X(A), where X ? {c0, c, lp} for 1 ? p ? ?. The other purpose of the present study is to introduce the sequence spaces X(A,?) = {x=(xk): (?x?k=1 an,kXk - ?x?k=1 an-1,kXk)? n=1 ? X}, where X ? {l1,c,c0}, and computing the NAB-(or Null) duals and ?AB-duals for these spaces.

scholarly journals Matrix transformations related to I-convergent sequences

2019 ◽  
Vol 22 (2) ◽  
pp. 191-200
Author(s):  
Enno Kolk
Keyword(s):  
Linear Operators ◽  
Matrix Transformations ◽  
Infinite Matrices ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Convergent Sequences

Characterized are matrix transformations related to certain subsets of the space of ideal convergent sequences. Obtained here results are connected with the previous investigations of the author on some transformations defined by infinite matrices of bounded linear operators.

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