scholarly journals The Expression of the Drazin Inverse with Rank Constraints

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Linlin Zhao
Keyword(s):  
Matrix Decomposition ◽  
Block Matrix ◽  
Drazin Inverse ◽  
Reverse Order ◽  
Reverse Order Law ◽  
The Matrix ◽  
Rank Constraints

By using the matrix decomposition and the reverse order law, we provide some new expressions of the Drazin inverse for any2×2block matrix with rank constraints.

Central Drazin inverses

2019 ◽  
Vol 18 (04) ◽  
pp. 1950065 ◽  
Author(s):  
Cang Wu ◽  
Liang Zhao
Keyword(s):  
Drazin Inverse ◽  
Reverse Order ◽  
Basic Properties ◽  
Reverse Order Law ◽  
Invertible Elements

We introduce and study a subclass of the Drazin invertible elements in a ring [Formula: see text], which are called central Drazin invertible. An element [Formula: see text] is said to be central Drazin invertible if there exists [Formula: see text] such that [Formula: see text], [Formula: see text] and [Formula: see text] for some integer [Formula: see text]. Some basic properties of the central Drazin inverse are obtained. Of particular interest are the central Drazin invertible elements that are simultaneously group invertible, which we show have a property generalizing strong cleanness. Some well-known results related to the cleanness of rings and the reverse order law are generalized.

scholarly journals Reverse order law of Drazin inverse for bounded linear operators

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4857-4864 ◽  
Author(s):  
Hua Wang ◽  
Junjie Huang
Keyword(s):  
Banach Space ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Reverse Order ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Reverse Order Law

In this paper, the reverse order law of Drazin inverse is investigated under some conditions in a Banach space. Moreover, the Drazin invertibility of sum for two bounded linear operators are also obtained.

Generalized Inverses

2021 ◽  
Vol 22 ◽  
pp. 13-32
Author(s):  
Dragan S. Djordjevic
Keyword(s):  
Generalized Inverses ◽  
Drazin Inverse ◽  
Reverse Order ◽  
Survey Paper ◽  
Reverse Order Law

In this survey paper we present some aspects of generalized inverses, which are related to inner and outer invertibility, Moore-Penrose inverse, the appropriate reverse order law, and Drazin inverse.

The Influence of Cu and Cr on the Matrix Decomposition of Quenched AlZnMg Alloy

1991 ◽  
Vol 124 (1) ◽  
pp. K11-K14 ◽  
Author(s):  
C. Dos Santos Lourenço ◽  
M. Cilense ◽  
W. Garlipp
Keyword(s):  
Matrix Decomposition ◽  
Mg Alloy ◽  
The Matrix

Identifying graph clusters using variational inference and links to covariance parametrization

2009 ◽  
Vol 367 (1906) ◽  
pp. 4407-4426
Author(s):  
David Barber
Keyword(s):  
Mean Field ◽  
Matrix Decomposition ◽  
Difficult Problem ◽  
Positive Definite ◽  
Variational Inference ◽  
Field Theories ◽  
Variational Approximation ◽  
Positive Definite Matrices ◽  
The Matrix ◽  
Non Gaussian

Finding clusters of well-connected nodes in a graph is a problem common to many domains, including social networks, the Internet and bioinformatics. From a computational viewpoint, finding these clusters or graph communities is a difficult problem. We use a clique matrix decomposition based on a statistical description that encourages clusters to be well connected and few in number. The formal intractability of inferring the clusters is addressed using a variational approximation inspired by mean-field theories in statistical mechanics. Clique matrices also play a natural role in parametrizing positive definite matrices under zero constraints on elements of the matrix. We show that clique matrices can parametrize all positive definite matrices restricted according to a decomposable graph and form a structured factor analysis approximation in the non-decomposable case. Extensions to conjugate Bayesian covariance priors and more general non-Gaussian independence models are briefly discussed.

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