scholarly journals New matrix domain derived by the matrix product

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1233-1241
Author(s):  
Vatan Karakaya ◽  
Necip Imşek ◽  
Kadri Doğan
Keyword(s):  
Topological Structure ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformation ◽  
Matrix Product ◽  
Difference Matrix ◽  
Matrix Domain ◽  
The Matrix ◽  
Necessary And Sufficient

In this work, we define new sequence spaces by using the matrix obtained by product of factorable matrix and generalized difference matrix of order m. Afterward, we investigate topological structure which are completeness, AK-property, AD-property. Also, we compute the ?-, ?- and ?- duals, and obtain bases for these sequence spaces. Finally we give necessary and sufficient conditions on matrix transformation between these new sequence spaces and c,??.

scholarly journals On the generalized Riesz B-difference sequence spaces

Filomat ◽  
2010 ◽  
Vol 24 (4) ◽  
pp. 35-52 ◽  
Author(s):  
Metin Başarir
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Difference Sequence ◽  
Topological Properties ◽  
Linear Spaces ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Difference Sequence Spaces

In this paper, we define the new generalized Riesz B-difference sequence spaces rq? (p, B), rqc (p, B), rq0 (p, B) and rq (p, B) which consist of the sequences whose Rq B-transforms are in the linear spaces l?(p), c (p), c0(p) and l(p), respectively, introduced by I.J. Maddox[8],[9]. We give some topological properties and compute the ?-, ?- and ?-duals of these spaces. Also we determine the necessary and sufficient conditions on the matrix transformations from these spaces into l? and c.

scholarly journals On mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product

2004 ◽  
Vol 2004 (58) ◽  
pp. 3103-3116 ◽  
Author(s):  
Yongge Tian
Keyword(s):  
Mixed Type ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Reverse Order ◽  
Matrix Product ◽  
Matrix Rank ◽  
Matrix Rank Method ◽  
The Matrix ◽  
Necessary And Sufficient

Some mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product are established. Necessary and sufficient conditions for these laws to hold are found by the matrix rank method. Some applications and extensions of these reverse-order laws to the weighted Moore-Penrose inverse are also given.

scholarly journals The application domain of difference type matrix D(r,0,s,0,t) on some sequence spaces

2020 ◽  
pp. 32-32
Author(s):  
Avinoy Paul ◽  
Binod Tripathy
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Application Domain ◽  
Topological Properties ◽  
Difference Type ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Matrix Mappings

In this paper we introduce new sequence spaces with the help of domain of matrix D(r,0,s,0,t), and study some of their topological properties. Further, we determine ? and ? duals of the new sequence spaces and finally, we establish the necessary and sufficient conditions for characterization of the matrix mappings.

scholarly journals The Forward Order Law for Least Squareg-Inverse of Multiple Matrix Products

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 277 ◽  
Author(s):  
Zhiping Xiong ◽  
Zhongshan Liu
Keyword(s):  
Generalized Inverse ◽  
Sufficient Conditions ◽  
Schur Complement ◽  
Necessary And Sufficient Conditions ◽  
Matrix Product ◽  
The Core ◽  
Matrix Products ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Generalized Schur Complement

The generalized inverse has many important applications in the aspects of the theoretic research of matrices and statistics. One of the core problems of the generalized inverse is finding the necessary and sufficient conditions of the forward order laws for the generalized inverse of the matrix product. In this paper, by using the extremal ranks of the generalized Schur complement, we obtain some necessary and sufficient conditions for the forward order laws A 1 { 1 , 3 } A 2 { 1 , 3 } ⋯ A n { 1 , 3 } ⊆ ( A 1 A 2 ⋯ A n ) { 1 , 3 } and A 1 { 1 , 4 } A 2 { 1 , 4 } ⋯ A n { 1 , 4 } ⊆ ( A 1 A 2 ⋯ A n ) { 1 , 4 } .

scholarly journals On some new paranormed sequence spaces defined by the matrix (D )(r,0,0,s)

2021 ◽  
Vol 40 (3) ◽  
pp. 779-796
Author(s):  
Avinoy Paul
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Topological Properties ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Matrix Mappings

In this paper, we introduce some new paranormed sequence spaces and study some topological properties. Further, we determine α, β and γ-duals of the new sequence spaces and finally, we establish the necessary and sufficient conditions for characterization of matrix mappings.

scholarly journals On circulant codes with prescribed distances

1977 ◽  
Vol 16 (3) ◽  
pp. 361-369
Author(s):  
M. Deza ◽  
Peter Eades
Keyword(s):  
Sufficient Conditions ◽  
Difference Sets ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Weighing Matrices ◽  
Cyclic Difference Sets ◽  
The Matrix ◽  
Circulant Codes ◽  
Necessary And Sufficient ◽  
Square Matrix

Necessary and sufficient conditions are given for a square matrix to te the matrix of distances of a circulant code. These conditions are used to obtain some inequalities for cyclic difference sets, and a necessary condition for the existence of circulant weighing matrices.

On the factorable spaces of absolutely p-summable, null, convergent, and bounded sequences

2021 ◽  
Vol 71 (6) ◽  
pp. 1375-1400
Author(s):  
Feyzi Başar ◽  
Hadi Roopaei
Keyword(s):  
Lower Bound ◽  
Sequence Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Matrix Transformations ◽  
Infinite Matrix ◽  
The Matrix ◽  
Alpha Beta ◽  
Necessary And Sufficient ◽  
Bounded Sequences

Abstract Let F denote the factorable matrix and X ∈ {ℓp , c 0, c, ℓ ∞}. In this study, we introduce the domains X(F) of the factorable matrix in the spaces X. Also, we give the bases and determine the alpha-, beta- and gamma-duals of the spaces X(F). We obtain the necessary and sufficient conditions on an infinite matrix belonging to the classes (ℓ p (F), ℓ ∞), (ℓ p (F), f) and (X, Y(F)) of matrix transformations, where Y denotes any given sequence space. Furthermore, we give the necessary and sufficient conditions for factorizing an operator based on the matrix F and derive two factorizations for the Cesàro and Hilbert matrices based on the Gamma matrix. Additionally, we investigate the norm of operators on the domain of the matrix F. Finally, we find the norm of Hilbert operators on some sequence spaces and deal with the lower bound of operators on the domain of the factorable matrix.

scholarly journals A note on Köthe-Toeplitz duals of certain sequence spaces and their matrix transformations

1995 ◽  
Vol 18 (4) ◽  
pp. 681-688 ◽  
Author(s):  
B. Choudhary ◽  
S. K. Mishra
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Necessary And Sufficient

In this paper we define the sequence spacesSℓ∞(p),Sc(p)andSc0(p)and determine the Köthe-Toeplitz duals ofSℓ∞(p). We also obtain necessary and sufficient conditions for a matrixAto mapSℓ∞(p)toℓ∞and investigate some related problems.

Inverse problem about two-spectra for finite Jacobi matrices with zero diagonal

2016 ◽  
Vol 24 (6) ◽  
Author(s):  
Adil Huseynov
Keyword(s):  
Inverse Problem ◽  
Finite Order ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Jacobi Matrices ◽  
The Matrix ◽  
Explicit Procedure ◽  
Necessary And Sufficient

AbstractThe necessary and sufficient conditions for solvability of the inverse problem about two-spectra for finite order real Jacobi matrices with zero-diagonal elements are established. An explicit procedure of reconstruction of the matrix from the two-spectra is given.

Further results on generalized inverses in rings with involution

2015 ◽  
Vol 30 ◽  
Author(s):  
N. Castro-Gonzalez ◽  
Jianlong Chen ◽  
Long Wang
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Generalized Inverses ◽  
Matrix Product ◽  
Explicit Formulas ◽  
Block Matrices ◽  
Unital Ring ◽  
Rings With Involution ◽  
Necessary And Sufficient

Let R be a unital ring with an involution. Necessary and sufficient conditions for the existence of the Bott-Duffin inverse of a in R relative to a pair of self-adjoint idempotents (e, f) are derived. The existence of a {1, 3}-inverse, {1, 4}-inverse, and the Moore-Penrose inverse of a matrix product is characterized, and explicit formulas for their computations are obtained. Some applications to block matrices over a ring are given.

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