Characterization of matrix classes

1980 ◽  
pp. 36-64
Author(s):  
Ivor J. Maddox
Keyword(s):  
Matrix Classes

scholarly journals On the Characterization of Some Classes of Four-Dimensional Matrices and Almost B-Summable Double Sequences

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Orhan Tug
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Double Sequences ◽  
Matrix Classes ◽  
Related Literature ◽  
Double Sequence Spaces

We firstly summarize the related literature about Br,s,t,u-summability of double sequence spaces and almost Br,s,t,u-summable double sequence spaces. Then we characterize some new matrix classes of Ls′:Cf, BLs′:Cf, and Ls′:BCf of four-dimensional matrices in both cases of 0<s′≤1 and 1<s′<∞, and we complete this work with some significant results.

scholarly journals Characterization of matrix classes involving some sets of sequences of fuzzy numbers

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6101-6112 ◽  
Author(s):  
Hemen Dutta ◽  
Jyotishmaan Gogoi
Keyword(s):  
Level Sets ◽  
Fuzzy Numbers ◽  
Extension Principle ◽  
New Approach ◽  
Matrix Classes ◽  
Sequences Of Fuzzy Numbers

In 1996, M. Stojakovic and Z. Stojakovic examined the convergence of a sequence of fuzzy numbers via Zadeh?s Extension Principle, which is quite difficult for practical use. In this paper, we utilize the notion ?-level sets to deal with convergence and summable related notions and adopted a relatively new approach to characterize matrix classes involving some sets of single sequences of fuzzy numbers. The approach is expected to be useful in dealing with characterization of several other matrix classes involving different kinds of sets of sequences of fuzzy numbers, single or multiple

scholarly journals Almost Sequence Spaces Derived by the Domain of the Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ali Karaisa ◽  
Ümıt Karabıyık
Keyword(s):  
Normed Space ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Schauder Basis ◽  
Matrix Classes ◽  
Almost Convergent Sequence ◽  
Inclusion Relations ◽  
The Matrix

By using , we introduce the sequence spaces , , and of normed space and -space and prove that , and are linearly isomorphic to the sequence spaces , , and , respectively. Further, we give some inclusion relations concerning the spaces , , and the nonexistence of Schauder basis of the spaces and is shown. Finally, we determine the - and -duals of the spaces and . Furthermore, the characterization of certain matrix classes on new almost convergent sequence and series spaces has exhaustively been examined.

scholarly journals Pseudo Schur complements, pseudo principal pivot transforms and their inheritance properties

2015 ◽  
Vol 30 ◽  
Author(s):  
K. Sivakumar ◽  
Ravindran G. ◽  
Kavita Bisht
Keyword(s):  
Schur Complement ◽  
Block Matrix ◽  
Comprehensive Treatment ◽  
Matrix Classes ◽  
Fundamental Properties ◽  
Schur Complements ◽  
Inheritance Properties ◽  
Extended Notion

Extensions of the Schur complement and the principal pivot transform, where the usual inverses are replaced by the Moore-Penrose inverse, are revisited. These are called the pseudo Schur complement and the pseudo principal pivot transform, respectively. First, a generalization of the characterization of a block matrix to be an M-matrix is extended to the nonnegativity of the Moore-Penrose inverse. A comprehensive treatment of the fundamental properties of the extended notion of the principal pivot transform is presented. Inheritance properties with respect to certain matrix classes are derived, thereby generalizing some of the existing results. Finally, a thorough discussion on the preservation of left eigenspaces by the pseudo principal pivot transformation is presented.

scholarly journals Difference sequence spaces

1998 ◽  
Vol 21 (4) ◽  
pp. 701-706 ◽  
Author(s):  
A. K. Gaur ◽  
Mursaleen
Keyword(s):  
Sequence Spaces ◽  
Difference Sequence ◽  
Matrix Classes ◽  
The Matrix ◽  
Difference Sequence Spaces

In [1]Sr(Δ):={x=(xk):(kr|Δxk|)k=1∞∈c0}forr≥1is studied. In this paper, we generalize this space toSr(p,Δ)for a sequence of strictly positive reals. We give a characterization of the matrix classes(Sr(p,Δ),ℓ∞)and(Sr(p,Δ),ℓ1).

scholarly journals Characterization of Some Matrix Classes Involving Paranormed Sequence Spaces

2006 ◽  
Vol 37 (2) ◽  
pp. 155-162 ◽  
Author(s):  
Binod Chandra Tripathy ◽  
Mausumi Sen
Keyword(s):  
General Setting ◽  
Sequence Spaces ◽  
Matrix Classes

In this article we characterize some matrix classes with one member as $ {m}(p) $ or $ {m}_0(p) $ or $ c(p) $ or $ c_0(p)$. Some of these results generalize the existing results. Some are new proved in the general setting.

Characterization of Matrix Classes Transforming Between Almost Sure Convergent Sequences of Complex Uncertain Variables

2021 ◽  
Vol 14 (03) ◽  
Author(s):  
Birojit Das ◽  
Piyali Debnath ◽  
Binod Chandra Tripathy
Keyword(s):  
Uncertainty Theory ◽  
Matrix Transformation ◽  
Matrix Classes ◽  
Uncertain Variables ◽  
Convergent Sequences

The study of uncertainty theory evolved and developed largely in the last decade. In this paper, we introduce the concept of summability and absolutely summability with respect to almost surely through matrix transformation of complex uncertain sequences and establish the interrelationship between these two concepts. In this context, applications of matrix transformation of complex uncertain sequences are also presented.

scholarly journals Characterization of some matrix classes involving some sets with speed

2018 ◽  
Vol 19 (2) ◽  
pp. 813 ◽  
Author(s):  
S. Das ◽  
H. Dutta
Keyword(s):  
Matrix Classes
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