scholarly journals The operator system of Toeplitz matrices

2021 ◽  
Vol 8 (32) ◽  
pp. 999-1023
Author(s):  
Douglas Farenick
Keyword(s):  
Toeplitz Matrix ◽  
Toeplitz Matrices ◽  
Matrix Analysis ◽  
Trigonometric Polynomials ◽  
Complex Matrices ◽  
Content Type ◽  
Operator System ◽  
Order Isomorphism ◽  
Positive Linear Map ◽  
Operator Systems

A recent paper of A. Connes and W.D. van Suijlekom [Comm. Math. Phys. 383 (2021), pp. 2021–2067] identifies the operator system of n × n n\times n Toeplitz matrices with the dual of the space of all trigonometric polynomials of degree less than n n . The present paper examines this identification in somewhat more detail by showing explicitly that the Connes–van Suijlekom isomorphism is a unital complete order isomorphism of operator systems. Applications include two special results in matrix analysis: (i) that every positive linear map of the n × n n\times n complex matrices is completely positive when restricted to the operator subsystem of Toeplitz matrices and (ii) that every linear unital isometry of the n × n n\times n Toeplitz matrices into the algebra of all n × n n\times n complex matrices is a unitary similarity transformation. An operator systems approach to Toeplitz matrices yields new insights into the positivity of block Toeplitz matrices, which are viewed herein as elements of tensor product spaces of an arbitrary operator system with the operator system of n × n n\times n complex Toeplitz matrices. In particular, it is shown that min and max positivity are distinct if the blocks themselves are Toeplitz matrices, and that the maximally entangled Toeplitz matrix ξ n \xi _n generates an extremal ray in the cone of all continuous n × n n\times n Toeplitz-matrix valued functions f f on the unit circle S 1 S^1 whose Fourier coefficients f ^ ( k ) \hat f(k) vanish for | k | ≥ n |k|\geq n . Lastly, it is noted that all positive Toeplitz matrices over nuclear C ∗ ^* -algebras are approximately separable.

scholarly journals Operator system quotients of matrix algebras and their tensor products

2012 ◽  
Vol 111 (2) ◽  
pp. 210 ◽  
Author(s):  
Douglas Farenick ◽  
Vern I. Paulsen
Keyword(s):  
Tensor Products ◽  
Operator System ◽  
Linear Map ◽  
Order Isomorphism ◽  
Matrix Algebras ◽  
C Algebras ◽  
Tridiagonal Matrices ◽  
Quotient Maps ◽  
Operator Systems ◽  
Affirmative Solution

{If} $\phi:\mathcal{S}\rightarrow\mathcal{T}$ is a completely positive (cp) linear map of operator systems and if $\mathcal{J}=\ker\phi$, then the quotient vector space $\mathcal{S}/\mathcal{J}$ may be endowed with a matricial ordering through which $\mathcal{S}/\mathcal{J}$ has the structure of an operator system. Furthermore, there is a uniquely determined cp map $\dot{\phi}:\mathcal{S}/\mathcal{J} \rightarrow\mathcal{T}$ such that $\phi=\dot{\phi}\circ q$, where $q$ is the canonical linear map of $\mathcal{S}$ onto $\mathcal{S}/\mathcal{J}$. The cp map $\phi$ is called a complete quotient map if $\dot{\phi}$ is a complete order isomorphism between the operator systems $\mathcal{S}/\mathcal{J}$ and $\mathcal{T}$. Herein we study certain quotient maps in the cases where $\mathcal{S}$ is a full matrix algebra or a full subsystem of tridiagonal matrices. Our study of operator system quotients of matrix algebras and tensor products has applications to operator algebra theory. In particular, we give a new, simple proof of Kirchberg's Theorem $\operatorname{C}^*(\mathbf{F}_\infty)\otimes_{\min}\mathcal{B}(\mathcal{H})=\operatorname{C}^*(\mathbf{F}_\infty)\otimes_{\max}\mathcal{B}(\mathcal{H})$, show that an affirmative solution to the Connes Embedding Problem is implied by various matrix-theoretic problems, and give a new characterisation of unital $\operatorname{C}^*$-algebras that have the weak expectation property.

scholarly journals The pseudo core inverse of a companion matrix

2018 ◽  
Vol 55 (3) ◽  
pp. 407-420
Author(s):  
Yuefeng Gao ◽  
Jianlong Chen ◽  
Pedro Patrício ◽  
Dingguo Wang
Keyword(s):  
Toeplitz Matrix ◽  
Toeplitz Matrices ◽  
Generalized Inverses ◽  
Companion Matrix ◽  
Complex Matrix ◽  
Complex Matrices ◽  
The Core ◽  
Core Inverse ◽  
Companion Matrices ◽  
Existence Criteria

The notion of core inverse was introduced by Baksalary and Trenkler for a complex matrix of index 1. Recently, the notion of pseudo core inverse extended the notion of core inverse to an element of an arbitrary index in *-rings; meanwhile, it characterized the core-EP inverse introduced by Manjunatha Prasad and Mohana for complex matrices, in terms of three equations. Many works have been done on classical generalized inverses of companion matrices and Toeplitz matrices. In this paper, we discuss existence criteria and formulae of the pseudo core inverse of a companion matrix over a *-ring. A {1,3}-inverse of a Toeplitz matrix plays an important role in that process.

scholarly journals Toeplitz nonnegative realization of spectra via companion matrices

2019 ◽  
Vol 7 (1) ◽  
pp. 230-245
Author(s):  
Macarena Collao ◽  
Mario Salas ◽  
Ricardo L. Soto
Keyword(s):  
Eigenvalue Problem ◽  
Half Plane ◽  
Toeplitz Matrix ◽  
Toeplitz Matrices ◽  
Nonnegative Matrix ◽  
Inverse Eigenvalue Problem ◽  
Complex Numbers ◽  
Inverse Eigenvalue ◽  
Companion Matrices ◽  
Solution Matrix

Abstract The nonnegative inverse eigenvalue problem (NIEP) is the problem of finding conditions for the existence of an n × n entrywise nonnegative matrix A with prescribed spectrum Λ = {λ1, . . ., λn}. If the problem has a solution, we say that Λ is realizable and that A is a realizing matrix. In this paper we consider the NIEP for a Toeplitz realizing matrix A, and as far as we know, this is the first work which addresses the Toeplitz nonnegative realization of spectra. We show that nonnegative companion matrices are similar to nonnegative Toeplitz ones. We note that, as a consequence, a realizable list Λ= {λ1, . . ., λn} of complex numbers in the left-half plane, that is, with Re λi≤ 0, i = 2, . . ., n, is in particular realizable by a Toeplitz matrix. Moreover, we show how to construct symmetric nonnegative block Toeplitz matrices with prescribed spectrum and we explore the universal realizability of lists, which are realizable by this kind of matrices. We also propose a Matlab Toeplitz routine to compute a Toeplitz solution matrix.

Constraints and opportunities facing construction organization in post-conflict condition in Afghanistan

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Qais Amarkhil ◽  
Emad Elwakil
Keyword(s):  
Matrix Analysis ◽  
Content Type ◽  
Construction Firms ◽  
Construction Companies ◽  
Post Conflict ◽  
Conflict Condition ◽  
Local Construction ◽  
And Performance ◽  
Construction Organization ◽  
Critical Constraints

Purpose Although there are many challenges and constraints for construction organization operation and performance in a post-conflict condition, there is insufficient construction project management literature. Therefore, the purpose of this paper is to identify a framework to understand and determine critical constraints and opportunities in a post-conflict condition facing local construction firms in Afghanistan. The proposed framework is composed of three major steps: identify and determine key performance indicators; identify challenges impacting organization operation and performance in post-conflict condition; determine critical constraints and opportunities based on prioritized performance measures; and organizational strength and weakness factors. Design/methodology/approach The strength, weakness, opportunities and threat matrix analysis has been used to determine post-conflict condition constraints and opportunities. Then the analytical hierarchy process has been used to prioritize the measures and identify the constraints and opportunities facing construction companies in a post-conflict situation. The mix-research method is applied to this study to analyse qualitative variables and quantitative variables obtained from the experts’ opinions and 51 filled questioners. Findings The study shows that there are a total of 11 critical constraints and three essential opportunities for construction companies that industry practitioners and policymakers should take into account while formulating the organizational strategy. Practical implications The developed framework will benefit construction companies in improving their performance and operation in after-conflict conditions. Originality/value This paper is the first to provide a comprehensive conceptualization of the challenges and constraints for construction organization operation and performance in a post-conflict condition. It also offers a novel conceptual framework to understand and determine critical constraints and opportunities in a post-conflict condition facing local construction firms in Afghanistan.

How supplier knowledge impacts on organizational capabilities and willingness

2018 ◽  
Vol 48 (1) ◽  
pp. 140-158
Author(s):  
Peyman Akhavan ◽  
Ali Shahabipour ◽  
Reza Hosnavi
Keyword(s):  
Partial Least Square ◽  
Least Square ◽  
Organizational Capabilities ◽  
Matrix Analysis ◽  
Knowledge Flow ◽  
Primary Data ◽  
Development Programs ◽  
Content Type ◽  
Performance Matrix ◽  
Structured Questionnaire

Purpose The purpose of this paper is to conduct a survey on the knowledge for supplier correlation with their capabilities and willingness as segmentation criteria. There are many contexts for sharing knowledge. What are more beneficial contexts? Design/methodology/approach After developing the research hypothesis, a structured questionnaire was adopted to gather primary data from suppliers. The draft questionnaire was sent to five academic and industry experts to comment on the content. Received feedback was used to change the layout of the questionnaire. Instead of the traditional partial least squares, the state-of- art consistent partial least square technique was put into practice. Findings By definition, knowledge for supplier has a large impact on supplier capabilities. The Important-Performance Matrix Analysis (IPMA) prioritizes the indicators and suggests to focus on knowledge sharing about manufacturing processes, development expertise and marketing expertise. Results showed that supplier willingness for sharing confidential knowledge and longtime relationship depends on development programs. Practical implications Having a communication mechanism for each of the partnerships’ specific contexts was suggested to maximize the knowledge flow. Originality/value For maximizing the knowledge flow and studying the effect on the segmentation criteria such as capability and willingness, the main contribution of the paper is to survey the supplier knowledge in depth. The IPMA was implemented to highlight the indicators.

Supply chain resilience for vaccines: review of modeling approaches in the context of the COVID-19 pandemic

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Maureen S. Golan ◽  
Benjamin D. Trump ◽  
Jeffrey C. Cegan ◽  
Igor Linkov
Keyword(s):  
Supply Chain ◽  
Supply Chains ◽  
Securities And Exchange Commission ◽  
Matrix Analysis ◽  
Stress Tests ◽  
Critical Function ◽  
Content Type ◽  
Supply Chain Resilience ◽  
Production And Distribution ◽  
The Face

PurposeDespite rapid success in bringing SARS-CoV-2 vaccines to distribution by multiple pharmaceutical corporations, supply chain failures in production and distribution can plague pandemic recovery. This review analyzes and addresses gaps in modeling supply chain resilience in general and specifically for vaccines in order to guide researchers and practitioners alike to improve critical function of vaccine supply chains in the face of inevitable disruptions.Design/methodology/approachSystematic review of the literature on modeling supply chain resilience from 2007 to 2020 is analyzed in tandem with the vaccine supply chain manufacturing literature. These trends are then used to apply a novel matrix analysis to seven Securities and Exchange Commission (SEC) annual filings of pharmaceutical corporations involved in COVID-19 vaccine manufacture and distribution.FindingsPharmaceutical corporations favor efficiency as they navigate regulatory, economic and other threats to their vaccine supply chains, neglecting resilience – absorption, adaptation and recovery from inevitable and unexpected disruptions. However, explicitly applying resilience analytics to the vaccine supply chain and further leveraging emerging network science tools found in the academic literature, such as artificial intelligence (AI), stress tests and digital twins, will help supply chain managers to better quantify efficiency/resilience tradeoffs across all associated networks/domains and support optimal system performance post disruption.Originality/valueThis is the first review addressing resilience analytics in vaccine supply chains and subsequent extension to operational management through novel matrix analyses of SEC Filings. The authors provide analyses and recommendations that facilitate resilience quantification capabilities for vaccine supply chain managers, regulatory agencies and corporate stakeholders and are especially relevant for pandemic response, including application to the SARS-CoV-2 vaccines.

Examining internet banking user’s continuance intention through the lens of technology continuance theory and task technology fit model

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Samar Rahi ◽  
Mazuri Abd Ghani
Keyword(s):  
User Satisfaction ◽  
Internet Banking ◽  
Perceived Usefulness ◽  
Matrix Analysis ◽  
Research Model ◽  
Continuance Intention ◽  
Content Type ◽  
Task Technology Fit ◽  
And Task ◽  
Expectation Confirmation

Purpose The long-term success of internet banking (IB) services is connected with continuous use. Therefore, examining factors which influence IB user continuance intention is important. Grounded in technology continuance theory, bank transparency and task technology fit (TTF) model, the purpose of this study is to develop a unified technology continuance model to investigate IB user continuance intention. Design/methodology/approach The research model was empirically tested with 348 responses. Respondents included in this study had prior experience with IB services. For hypotheses testing, the structural equation modelling approach was used. Findings Findings indicate that the research model has substantial power in explaining IB user continuance intention. Importance performance matrix analysis revealed that bank transparency had the highest importance in determining IB user continuance intention. Therefore, factors like user satisfaction and perceived usefulness have shown a medium level of importance in determining IB user continuance intention. Satisfaction is influenced by perceived usefulness and confirmation and established a significant impact on IB user continuance intention. Practical implications The findings of this research are useful for bank managers and policymakers to develop and design IB services according to user’s expectations. Results demonstrate that expectation confirmation and perceived usefulness are antecedents of IB user satisfaction and IB user continuance intention. In addition to that bank, transparency has shown a significant effect on user expectation and IB user continuance intention. These findings established that accuracy in sharing bank information and clarity in transaction charges encourage the user to continue the use of IB services. Originality/value The current study develops a unified technology continuance model based on the TTF model and technology continuance theory and investigates IB user continuance intention. Moreover, bank transparency is added in the technology continuance model and established a significant impact towards user expectation confirmation and continuance intention. These findings contribute to the limited body of research in the context of IB user continuance intention and enrich information system literature.

A new insight into alumni satisfaction model for Islamic higher education institutions (IHEI)

2018 ◽  
Vol 41 (12) ◽  
pp. 1411-1437 ◽  
Author(s):  
Abdur Rafik ◽  
Anjar Priyono
Keyword(s):  
Higher Education ◽  
Service Quality ◽  
Structural Equation ◽  
Higher Education Institutions ◽  
Equation Model ◽  
Partial Least Square ◽  
Least Square ◽  
Matrix Analysis ◽  
Content Type ◽  
Satisfaction Model

Purpose The purpose of this study is to explore and decompose a satisfaction model using alumni’s perspective for Islamic-based higher education institutions (IHEI) with the antecedent of perceived quality and value and the consequence of loyalty. Design/methodology/approach A study was used, using 44-item, a ten-point Likert-scale questionnaire administered to 360 alumni from various classes started from the 1970s till 2000s. Theoretical-based, national qualification framework of Indonesian higher education and management-based considerations were involved in developing a survey. Data were analyzed using partial least square-structural equation model and decomposed into strategic management map using importance-performance matrix analysis. Findings The most important determinants of alumni satisfaction and loyalty in IHEI is the IHEI’s ability to develop career capability through enriching knowledge. Moreover, the presence of good environment and Islamic value embodiment supporting learning programs on campus is the most significant trigger for the knowledge development. Research limitations/implications The results were generated from a specific department. Additional studies are needed to test if the results are not department (institution)-specific. Practical implications This study provides strategic directions for management to improve the critical aspects of the system by providing the inputs to the extent to which the service quality delivered may contribute to end-customers’ satisfaction. Originality/value It contributes to the literature on satisfaction and service quality issues by incorporating ideological aspect, by investigating the feasible model of customer satisfaction in the perspective of alumni for IHEI.

An approximation property for operator systems

2019 ◽  
Vol 22 (01) ◽  
pp. 1950005
Author(s):  
Wei Wu
Keyword(s):  
Tensor Product ◽  
Convex Sets ◽  
Approximation Property ◽  
Tensor Products ◽  
Order Unit ◽  
Operator System ◽  
Operator Systems ◽  
Natural Sense

Motivated by an observation of Namioka and Phelps on an approximation property of order unit spaces, we introduce the [Formula: see text]-tensor product and the [Formula: see text]-tensor product of two compact matrix convex sets. We define a new approximation property for operator systems, and give a characterization using the [Formula: see text]- and [Formula: see text]-tensor products in the spirit of Grothendieck. Thus, an operator system has the operator system approximation property if and only if it is [Formula: see text]-nuclear in a natural sense.

scholarly journals The ZKIR Assay, a Real-Time PCR Method for the Detection of Klebsiella pneumoniae and Closely Related Species in Environmental Samples

2020 ◽  
Vol 86 (7) ◽  
Author(s):  
Elodie Barbier ◽  
Carla Rodrigues ◽  
Geraldine Depret ◽  
Virginie Passet ◽  
Laurent Gal ◽  
...  
Keyword(s):  
Public Health ◽  
Klebsiella Pneumoniae ◽  
Real Time ◽  
Real Time Pcr ◽  
Environmental Samples ◽  
Health Concern ◽  
Complex Matrices ◽  
Content Type ◽  
Novel Method ◽  
Pcr Method

ABSTRACT Klebsiella pneumoniae is of growing public health concern due to the emergence of strains that are multidrug resistant, virulent, or both. Taxonomically, the K. pneumoniae complex (“Kp”) includes seven phylogroups, with Kp1 (K. pneumoniae sensu stricto) being medically prominent. Kp can be present in environmental sources such as soils and vegetation, which could act as reservoirs of animal and human infections. However, the current lack of screening methods to detect Kp in complex matrices limits research on Kp ecology. Here, we analyzed 1,001 genome sequences and found that existing molecular detection targets lack specificity for Kp. A novel real-time PCR method, the ZKIR (zur-khe intergenic region) assay, was developed and used to detect Kp in 96 environmental samples. The results were compared to a culture-based method using Simmons citrate agar with 1% inositol medium coupled to matrix-assisted laser desorption ionization–time of flight mass spectrometry identification. Whole-genome sequencing of environmental Kp was performed. The ZKIR assay was positive for the 48 tested Kp reference strains, whereas 88 non-Kp strains were negative. The limit of detection of Kp in spiked soil microcosms was 1.5 × 10−1 CFU g−1 after enrichment for 24 h in lysogeny broth supplemented with ampicillin, and it was 1.5 × 103 to 1.5 × 104 CFU g−1 directly after soil DNA extraction. The ZKIR assay was more sensitive than the culture method. Kp was detected in 43% of environmental samples. Genomic analysis of the isolates revealed a predominance of phylogroups Kp1 (65%) and Kp3 (32%), a high genetic diversity (23 multilocus sequence types), a quasi-absence of antibiotic resistance or virulence genes, and a high frequency (50%) of O-antigen type 3. This study shows that the ZKIR assay is an accurate, specific, and sensitive novel method to detect the presence of Kp in complex matrices and indicates that Kp isolates from environmental samples differ from clinical isolates. IMPORTANCE The Klebsiella pneumoniae species complex Kp includes human and animal pathogens, some of which are emerging as hypervirulent and/or antibiotic-resistant strains. These pathogens are diverse and classified into seven phylogroups, which may differ in their reservoirs and epidemiology. Proper management of this public health hazard requires a better understanding of Kp ecology and routes of transmission to humans. So far, detection of these microorganisms in complex matrices such as food or the environment has been difficult due to a lack of accurate and sensitive methods. Here, we describe a novel method based on real-time PCR which enables detection of all Kp phylogroups with high sensitivity and specificity. We used this method to detect Kp isolates from environmental samples, and we show based on genomic sequencing that they differ in antimicrobial resistance and virulence gene content from human clinical Kp isolates. The ZKIR PCR assay will enable rapid screening of multiple samples for Kp presence and will thereby facilitate tracking the dispersal patterns of these pathogenic strains across environmental, food, animal and human sources.

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