A Gersgorin Inclusion Set for the Field of Values of a Finite Matrix

1973 ◽  
Vol 41 (1) ◽  
pp. 57
Author(s):  
Charles R. Johnson
Keyword(s):  
Finite Matrix ◽  
Field Of Values ◽  
Inclusion Set

Limits for the Field of Values of a Matrix

1945 ◽  
Vol 52 (9) ◽  
pp. 488-493 ◽  
Author(s):  
A. B. Farnell
Keyword(s):  
Field Of Values

scholarly journals Exact relation between singular value and eigenvalue statistics

2016 ◽  
Vol 05 (04) ◽  
pp. 1650015 ◽  
Author(s):  
Mario Kieburg ◽  
Holger Kösters
Keyword(s):  
Singular Values ◽  
Singular Value ◽  
Specific Class ◽  
Rotation Invariant ◽  
Exact Relation ◽  
Finite Matrix ◽  
Eigenvalue Statistics ◽  
Probability Densities ◽  
Analytical Relations ◽  
Matrix Spaces

We use classical results from harmonic analysis on matrix spaces to investigate the relation between the joint densities of the singular values and the eigenvalues for complex random matrices which are bi-unitarily invariant (also known as isotropic or unitary rotation invariant). We prove that each of these joint densities determines the other one. Moreover, we construct an explicit formula relating both joint densities at finite matrix dimension. This relation covers probability densities as well as signed densities. With the help of this relation we derive general analytical relations among the corresponding kernels and biorthogonal functions for a specific class of polynomial ensembles. Furthermore, we show how to generalize the relation between the singular value and eigenvalue statistics to certain situations when the ensemble is deformed by a term which breaks the bi-unitary invariance.

Speech Influence Mechanisms and Models in Polycode and Polymodal Text (Using the Example of Regional Television Sports Coverage)

2021 ◽  
Vol 10 (1) ◽  
pp. 72-76
Author(s):  
Elina Nikitina
Keyword(s):  
Information Sharing ◽  
New Knowledge ◽  
Field Of Values ◽  
Sports Coverage ◽  
Points Of View

This article analyzes speech influence mechanisms and models in polycode and polymodal text. As an example, we took a sports coverages aired on regional television, since it is a polycode and polymodal composing. The publication presents speech influence mechanisms and models proposed by various researchers. Taking into consideration various points of view it can be assumed that speech influence in television sports coverage occurs through the information sharing on two levels proposed by A.A. Leontiev. This process is carried out either by introducing new knowledge about reality into the field of values of the recipient, on the basis of which he will change his behavior or his attitude to this reality, or by changing the field of values of the recipient without introducing new elements.

New Parameterizations of \(\mathrm{SL}(2,\mathbb{R})\) and Some Explicit Formulas for Its Logarithm

2021 ◽  
Vol 60 ◽  
pp. 65-81
Author(s):  
Tihomir Valchev ◽  
◽  
Clementina Mladenova ◽  
Ivaïlo Mladenov
Keyword(s):  
Lie Groups ◽  
Analytic Description ◽  
Exponential Map ◽  
Explicit Formulas ◽  
Field Of Values

Here we demonstrate some of the benefits of a novel parameterization of the Lie groups $\mathrm{Sp}(2,\bbr)\cong\mathrm{SL}(2,\bbr)$. Relying on the properties of the exponential map $\mathfrak{sl}(2,\bbr)\to\mathrm{SL}(2,\bbr)$, we have found a few explicit formulas for the logarithm of the matrices in these groups.\\ Additionally, the explicit analytic description of the ellipse representing their field of values is derived and this allows a direct graphical identification of various types.

Elastothermodynamic Damping of Fiber-Reinforced Metal-Matrix Composites

1995 ◽  
Vol 62 (2) ◽  
pp. 441-449 ◽  
Author(s):  
K. B. Milligan ◽  
V. K. Kinra
Keyword(s):  
Metal Matrix Composites ◽  
Metal Matrix ◽  
Axial Strain ◽  
Second Law Of Thermodynamics ◽  
Infinite Matrix ◽  
Matrix Composites ◽  
Fiber Reinforced ◽  
Continuous Fiber ◽  
Finite Matrix ◽  
Starting Point

Recently, taking the second law of thermodynamics as a starting point, a theoretical framework for an exact calculation of the elastothermodynamic damping in metal-matrix composites has been presented by the authors (Kinra and Milligan, 1994; Milligan and Kinra, 1993). Using this work as a foundation, we solve two canonical boundary value problems concerning elastothermodynamic damping in continuous-fiber-reinforced metal-matrix composites: (1) a fiber in an infinite matrix, and (2) using the general methodology given by Bishop and Kinra (1993), a fiber in a finite matrix. In both cases the solutions were obtained for the following loading conditions: (1) uniform radial stress and (2) uniform axial strain.

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