On the matrix representation of closed linear operators: An extension of the Von Neumann’s theory

1979 ◽  
Vol 20 (1) ◽  
pp. 148-152 ◽  
Author(s):  
G. Epifanio ◽  
C. Trapani
Keyword(s):  
Matrix Representation ◽  
Linear Operators ◽  
The Matrix ◽  
Closed Linear Operators

scholarly journals On linear operators for which TTD is normal

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2695-2704
Author(s):  
Ramesh Yousefi ◽  
Mansour Dana
Keyword(s):  
Matrix Representation ◽  
Normal Operator ◽  
Invertible Operator ◽  
Linear Operators ◽  
Commutativity Theorem ◽  
Normal Matrices ◽  
Basic Properties ◽  
The Matrix ◽  
Normal Operators ◽  
Drazin Invertible Operator

A Drazin invertible operator T ? B(H) is called skew D-quasi-normal operator if T* and TTD commute or equivalently TTD is normal. In this paper, firstly we give a list of conditions on an operator T; each of which is equivalent to T being skew D-quasi-normal. Furthermore, we obtain the matrix representation of these operators. We also develop some basic properties of such operators. Secondly we extend the Kaplansky theorem and the Fuglede-Putnam commutativity theorem for normal operators to skew D-quasi-normal matrices.

Spectral value sets of closed linear operators

2000 ◽  
Vol 456 (1998) ◽  
pp. 1397-1418 ◽  
Author(s):  
E. Gallestey ◽  
D. Hinrichsen ◽  
A. J. Pritchard
Keyword(s):  
Linear Operators ◽  
Value Sets ◽  
Closed Linear Operators

MRHS solver based on linear algebra and exhaustive search

2018 ◽  
Vol 12 (3) ◽  
pp. 143-157 ◽  
Author(s):  
Håvard Raddum ◽  
Pavol Zajac
Keyword(s):  
Linear Algebra ◽  
Matrix Representation ◽  
Equation System ◽  
Exhaustive Search ◽  
Binary Matrix ◽  
Algebraic Attacks ◽  
The Matrix ◽  
Speed Up ◽  
Symmetric Key

Abstract We show how to build a binary matrix from the MRHS representation of a symmetric-key cipher. The matrix contains the cipher represented as an equation system and can be used to assess a cipher’s resistance against algebraic attacks. We give an algorithm for solving the system and compute its complexity. The complexity is normally close to exhaustive search on the variables representing the user-selected key. Finally, we show that for some variants of LowMC, the joined MRHS matrix representation can be used to speed up regular encryption in addition to exhaustive key search.

scholarly journals On Stable Perturbations of the Generalized Drazin Inverses of Closed Linear Operators in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Qianglian Huang ◽  
Lanping Zhu ◽  
Xiaoru Chen ◽  
Chang Zhang
Keyword(s):  
Banach Spaces ◽  
Null Space ◽  
Linear Operators ◽  
Special Cases ◽  
Stable Perturbation ◽  
Closed Linear Operators

We investigate the stable perturbation of the generalized Drazin inverses of closed linear operators in Banach spaces and obtain some new characterizations for the generalized Drazin inverses to have prescribed range and null space. As special cases of our results, we recover the perturbation theorems of Wei and Wang, Castro and Koliha, Rakocevic and Wei, Castro and Koliha and Wei.

Molecular and morphometric characterisation of Xiphinema globosum Sturhan, 1978 (Nematoda: Longidoridae) from Spain

Nematology ◽  
2011 ◽  
Vol 13 (1) ◽  
pp. 17-28 ◽  
Author(s):  
Blanca Landa ◽  
Carolina Cantalapiedra-Navarrete ◽  
Juan Palomares-Rius ◽  
Pablo Castillo ◽  
Carlos Gutiérrez-Gutiérrez
Keyword(s):  
Phylogenetic Trees ◽  
18S Rrna ◽  
Matrix Representation ◽  
Natural Environments ◽  
28S Rrna ◽  
Parsimony Method ◽  
Rdna Genes ◽  
Supertree Method ◽  
The Matrix ◽  
Relationship Of

AbstractDuring a recent nematode survey in natural environments of the Los Alcornocales Regional Park narrow valleys, viz., the renowned 'canutos' excavated in the mountains that maintain a humid microclimate, in southern Spain, an amphimictic population of Xiphinema globosum was identified. Morphological and morphometric studies on this population fit the original and previous descriptions and represent the first report from Spain and southern Europe. Molecular characterisation of X. globosum from Spain using D2-D3 expansion regions of 28S rRNA, 18S rRNA and ITS1-rRNA is provided and maximum likelihood and Bayesian inference analysis were used to reconstruct phylogenetic relationships within X. globosum and other Xiphinema species. A supertree solution of the different phylogenetic trees obtained in this study and in other published studies using rDNA genes are presented using the matrix representation parsimony method (MRP) and the most similar supertree method (MSSA). The results revealed a closer phylogenetic relationship of X. globosum with X. diversicaudatum, X. bakeri and with some sequences of unidentified Xiphinema spp. deposited in GenBank.

Leontev Input-Output Balance Model as a Dynamic System Control Problem

2021 ◽  
pp. 66-82
Author(s):  
S.N. Masaev
Keyword(s):  
Dynamic System ◽  
Matrix Representation ◽  
External Environment ◽  
Balance Model ◽  
System Control ◽  
Operational Mode ◽  
Input Output ◽  
System A ◽  
The Matrix ◽  
Research Show

The purpose of the study was to determine the problem of control of a dynamic system of higher dimension. Relying on Leontev input-output balance, we formalized the dynamic system and synthesized its control. Within the research, we developed a mathematical model that combines different working objects that consume and release various resources. The value of the penalty for all nodes and objects is introduced into the matrix representation of the problem, taking into account various options for their interaction, i.e., the observation problem. A matrix representation of the planning task at each working object is formed. For the formed system, a control loop is created; the influencing parameters of the external environment are indicated. We calculated the system operational mode, taking into account the interaction of the nodes of objects with each other when the parameters of the external environment influence them. Findings of research show that in achieving a complex result, the system is inefficient without optimal planning and accounting for the matrix of penalties for the interaction of nodes and objects of the dynamic system with each other. In a specific example, for a dynamic system with a dimension of 4.8 million parameters, we estimated the control taking into account the penalty matrix, which made it possible to increase the inflow of additional resources from the outside by 2.4 times from 130 billion conv. units up to 310 conv. units in 5 years. Taking into account the maximum optimization of control in the nodes, an increase of 3.66 times in the inflow of additional resources was ensured --- from 200.46 to 726.62 billion rubles

Matrix representation of formal polynomials over max-plus algebra

2020 ◽  
pp. 2150216
Author(s):  
Cailu Wang ◽  
Yuegang Tao
Keyword(s):  
Matrix Method ◽  
Polynomial Algorithm ◽  
Polynomial Function ◽  
Matrix Representation ◽  
Sufficient Condition ◽  
Polynomial Functions ◽  
Canonical Forms ◽  
Necessary And Sufficient Condition ◽  
The Matrix ◽  
Necessary And Sufficient

This paper proposes the matrix representation of formal polynomials over max-plus algebra and obtains the maximum and minimum canonical forms of a polynomial function by standardizing this representation into a canonical form. A necessary and sufficient condition for two formal polynomials corresponding to the same polynomial function is derived. Such a matrix method is constructive and intuitive, and leads to a polynomial algorithm for factorization of polynomial functions. Some illustrative examples are presented to demonstrate the results.

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