scholarly journals Power partial isometry index and ascent of a finite matrix

2014 ◽  
Vol 459 ◽  
pp. 136-144 ◽  
Author(s):  
Hwa-Long Gau ◽  
Pei Yuan Wu
Keyword(s):  
Partial Isometry ◽  
Finite Matrix

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.

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.

scholarly journals Some characterizations of partial isometry elements in rings with involutions

Filomat ◽  
2019 ◽  
Vol 33 (19) ◽  
pp. 6395-6399
Author(s):  
Yinchun Qu ◽  
Hua Yao ◽  
Junchao Wei
Keyword(s):  
Partial Isometry ◽  
Necessary Conditions ◽  
Sufficient And Necessary Conditions

We give some sufficient and necessary conditions for an element in a ring with involution to be a partial isometry by using certain equations admitting solutions in a definite set.

scholarly journals Modules with Chain Conditions for Finite Matrix Subgroups

1997 ◽  
Vol 190 (1) ◽  
pp. 68-87 ◽  
Author(s):  
Wolfgang Zimmermann
Keyword(s):  
Chain Conditions ◽  
Finite Matrix

Central Sequence Algebras of a Purely Infinite Simple C*-algebra

2004 ◽  
Vol 56 (6) ◽  
pp. 1237-1258 ◽  
Author(s):  
Akitaka Kishimoto
Keyword(s):  
Fixed Point ◽  
Partial Isometry ◽  
Characterization Result ◽  
C Algebra ◽  
Central Sequence ◽  
Sequence Algebra ◽  
K Theory

AbstractWe are concerned with a unital separable nuclear purely infinite simple C*-algebra A satisfying UCT with a Rohlin flow, as a continuation of [12]. Our first result (which is independent of the Rohlin flow) is to characterize when two central projections in A are equivalent by a central partial isometry. Our second result shows that the K-theory of the central sequence algebra A′ ∩ Aω (for an ω ∈ βN\N) and its fixed point algebra under the flow are the same (incorporating the previous result). We will also complete and supplement the characterization result of the Rohlin property for flows stated in [12].

scholarly journals A note on the Ritz method with an application to overtone stellar pulsation theory

1968 ◽  
Vol 8 (2) ◽  
pp. 275-286 ◽  
Author(s):  
A. L. Andrew
Keyword(s):  
Numerical Solution ◽  
Eigenvalue Problems ◽  
Ritz Method ◽  
Linear Operators ◽  
Matrix Equations ◽  
Infinite Dimensional ◽  
Stellar Pulsation ◽  
Finite Matrix ◽  
The Matrix ◽  
Matrix Eigenvalue Problems

The Ritz method reduces eigenvalue problems involving linear operators on infinite dimensional spaces to finite matrix eigenvalue problems. This paper shows that for a certain class of linear operators it is possible to choose the coordinate functions so that numerical solution of the matrix equations is considerably simplified, especially when the matrices are large. The method is applied to the problem of overtone pulsations of stars.

A Combinatorial method for a class of matrix games

1966 ◽  
Vol 3 (2) ◽  
pp. 495-511
Author(s):  
Rodrigo A. Restrepo
Keyword(s):  
Optimal Strategies ◽  
Matrix Game ◽  
Combinatorial Method ◽  
Matrix Games ◽  
Finite Matrix ◽  
Special Relations ◽  
Class Of Matrices

The optimal strategies of any finite matrix game can be characterized by means of the Snow-Shapley Theorem [1]. However, in order to use this theorem to compute the optimal strategies, it may be necessary to invert a large number of matrices, most of which are not related to the solutions of the game. The present paper will show that when the columns of the pay-off matrix satisfy some special relations, it is possible to enumerate a much smaller class of matrices from which the optimal strategies may be obtained. Furthermore, the maximizing strategies that are determined by these matrices can be written down by inspection as soon as the matrices are specified.

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