Block-Structure Relocation via State and State Derivative Feedback Eigenspace of Matrix Polynomials Characterization

2016 ◽  
Vol 4 (1) ◽  
pp. 95-111 ◽  
Author(s):  
Belkacem Bekhiti ◽  
Abdelhakim Dahimene ◽  
Bachir Nail ◽  
Kamel Hariche
Keyword(s):  
Block Structure ◽  
Matrix Polynomials

scholarly journals Explicit Block-Structures for Block-Symmetric Fiedler-like pencils

2018 ◽  
Vol 34 ◽  
pp. 472-499 ◽  
Author(s):  
M. I. Bueno ◽  
Madeline Martin ◽  
Javier Perez ◽  
Alexander Song ◽  
Irina Viviano
Keyword(s):  
Matrix Polynomial ◽  
Block Structure ◽  
Canonical Forms ◽  
Complex Matrix ◽  
Main Obstacle ◽  
Matrix Polynomials ◽  
Structured Matrix ◽  
Symmetric Structure ◽  
The Family ◽  
Block Structures

In the last decade, there has been a continued effort to produce families of strong linearizations of a matrix polynomial $P(\lambda)$, regular and singular, with good properties, such as, being companion forms, allowing the recovery of eigenvectors of a regular $P(\lambda)$ in an easy way, allowing the computation of the minimal indices of a singular $P(\lambda)$ in an easy way, etc. As a consequence of this research, families such as the family of Fiedler pencils, the family of generalized Fiedler pencils (GFP), the family of Fiedler pencils with repetition, and the family of generalized Fiedler pencils with repetition (GFPR) were constructed. In particular, one of the goals was to find in these families structured linearizations of structured matrix polynomials. For example, if a matrix polynomial $P(\lambda)$ is symmetric (Hermitian), it is convenient to use linearizations of $P(\lambda)$ that are also symmetric (Hermitian). Both the family of GFP and the family of GFPR contain block-symmetric linearizations of $P(\lambda)$, which are symmetric (Hermitian) when $P(\lambda)$ is. Now the objective is to determine which of those structured linearizations have the best numerical properties. The main obstacle for this study is the fact that these pencils are defined implicitly as products of so-called elementary matrices. Recent papers in the literature had as a goal to provide an explicit block-structure for the pencils belonging to the family of Fiedler pencils and any of its further generalizations to solve this problem. In particular, it was shown that all GFP and GFPR, after permuting some block-rows and block-columns, belong to the family of extended block Kronecker pencils, which are defined explicitly in terms of their block-structure. Unfortunately, those permutations that transform a GFP or a GFPR into an extended block Kronecker pencil do not preserve the block-symmetric structure. Thus, in this paper, the family of block-minimal bases pencils, which is closely related to the family of extended block Kronecker pencils, and whose pencils are also defined in terms of their block-structure, is considered as a source of canonical forms for block-symmetric pencils. More precisely, four families of block-symmetric pencils which, under some generic nonsingularity conditions are block minimal bases pencils and strong linearizations of a matrix polynomial, are presented. It is shown that the block-symmetric GFP and GFPR, after some row and column permutations, belong to the union of these four families. Furthermore, it is shown that, when $P(\lambda)$ is a complex matrix polynomial, any block-symmetric GFP and GFPR is permutationally congruent to a pencil in some of these four families. Hence, these four families of pencils provide an alternative but explicit approach to the block-symmetric Fiedler-like pencils existing in the literature.

The Moving-IAT

2017 ◽  
Vol 33 (6) ◽  
pp. 445-452
Author(s):  
Monika Fleischhauer
Keyword(s):  
Internal Consistency ◽  
Personality Assessment ◽  
Block Structure ◽  
Mental Representations ◽  
Indirect Measures ◽  
Attitude Research ◽  
Self Reports ◽  
Implicit Personality ◽  
Single Block ◽  
Psychometric Quality

Abstract. Accumulated evidence suggests that indirect measures such as the Implicit Association Test (IAT) provide an increment in personality assessment explaining behavioral variance over and above self-reports. Likewise, it has been shown that there are several unwanted sources of variance in personality IATs potentially reducing their psychometric quality. For example, there is evidence that individuals use imagery-based facilitation strategies while performing the IAT. That is, individuals actively create mental representations of their person that fit to the category combination in the respective block, but do not necessarily fit to their implicit personality self-concept. A single-block IAT variant proposed by attitude research, where compatible and incompatible trials are presented in one and the same block, may prevent individuals from using such facilitation strategies. Consequently, for the trait need for cognition (NFC), a new single-block IAT version was developed (called Moving-IAT) and tested against the standard IAT for differences in internal consistency and predictive validity in a sample of 126 participants. Although the Moving-IAT showed lower internal consistency, its predictive value for NFC-typical behavior was higher than that of the standard IAT. Given individual’s strategy reports, the single-block structure of the Moving-IAT indeed reduces the likelihood of imagery-based strategies.

Matching Design of Tram Flexible Block Structure and Material

CICTP 2020 ◽  
2020 ◽  
Author(s):  
Wanqing Zhang ◽  
Jinyan Zhu ◽  
Ying Cheng ◽  
Chen Liu ◽  
Rongchun Shi
Keyword(s):  
Block Structure ◽  
Matching Design

A general inverse matrix series relation and associated polynomials – II

2021 ◽  
Vol 71 (2) ◽  
pp. 301-316
Author(s):  
Reshma Sanjhira
Keyword(s):  
Matrix Polynomial ◽  
Combinatorial Identities ◽  
Inverse Matrix ◽  
Matrix Polynomials ◽  
Special Cases ◽  
Series Representations ◽  
The Matrix ◽  
Associated Polynomials ◽  
Matrix Pair ◽  
Matrix Series

Abstract We propose a matrix analogue of a general inverse series relation with an objective to introduce the generalized Humbert matrix polynomial, Wilson matrix polynomial, and the Rach matrix polynomial together with their inverse series representations. The matrix polynomials of Kiney, Pincherle, Gegenbauer, Hahn, Meixner-Pollaczek etc. occur as the special cases. It is also shown that the general inverse matrix pair provides the extension to several inverse pairs due to John Riordan [An Introduction to Combinatorial Identities, Wiley, 1968].

Cluster and building block structure of amylopectin from waxy maize starch

2021 ◽  
Author(s):  
Yajuan Wang ◽  
Jin Qian ◽  
Di Liu ◽  
Mengwen Sun ◽  
Hui Chen ◽  
...  
Keyword(s):  
Building Block ◽  
Block Structure ◽  
Maize Starch ◽  
Waxy Maize
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