Generalized Inverses
A survey of generalized inverses and their use in stochastic modelling
... Generalized inverses play an important role in the solution of such singular sets of ...of generalized inverses to the aforementioned ...of generalized inverses associated with ...
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Equalities and inequalities for ranks of products of generalized inverses of two matrices and their applications
... between generalized inverses of matrices and rank formulas of matrices were recognized in the s, and a seminal work on rank formulas for matrices and their generalized inverses was ...
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Linear statistical models, least-squares estimators, and classification analysis to reverse-order laws for generalized inverses of matrix products
... of generalized inverses in many ...involves generalized inverses, one of the most fundamental fact people like to know is concerned with the invariance property of the matrix expression with ...
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A family of 512 reverse order laws for generalized inverses of two matrix product: a review Yongge Tian
... of generalized inverses of A, B, and AB through use of the definitions of generalized inverses, the block matrix method, the matrix equation method, and the matrix rank ...involve ...
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Further results on a matrix equality and matrix set inclusions for generalized inverses of matrix products Yongge Tian
... by inverses and generalized inverses of matrices from theoretical and applied points of ...for generalized inverses of matrix ...
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Generalized inverses, stationary distributions and mean first passage times with applications to perturbed Markov chains
... Since, as we shall see later, the derivation of mean first passage times involves either the computation of a matrix inverse or a matrix generalized inverse, we consider those techniques for solving the stationary ...
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Inequalities for ranks of matrix expressions involving generalized inverses
... The inequalities for ranks of a matrix expression play the important roles in matrix the- ory for describing the dimension of the row and column vector space of the matrix expres- sions, which are well understand and are ...
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The SMW Formula for Bounded Homogeneous Generalized Inverses with Applications
... Over the years, Generalizations (see [1] [2] for example) have been considered in the case of singular or rectangular matrices using the concept of Moore-Penrose generalized inverses. Certain results on ...
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Properties on Some Types of Generalized Inverses of Matrices-A Review
... the Generalized Inverses appear different uses and fields such as in science , statistics and engineering , such as least squares parataxis, unique differential and vary neutralization , Markov chains, its ...
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Simple procedures for finding mean first passage times in Markov chains
... suitable generalized inverses of the Markovian kernel I – P, where P is the transition matrix of a finite irreducible Markov chain, we are able to derive elegant new results for finding the mean first ...
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New results on the quasi-commuting inverses
... different generalized inverses for different ...the generalized inverse, play major role in solving consistent or inconsistent singular linear system [2, 5, ...
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Natural Generalized Inverse and Core of an Element in Semigroups, Rings and Banach and Operator algebras
... We say a is (von Neumann) regular in S if a ∈ aSa. A particular solution to a x a = a is called an associate, or inner inverse, of a. A solution to x a x = a is called a weak (or outer) inverse. Finally, an element that ...
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Fuzzy Relational Equations of k-Regular Block Fuzzy Matrices
... Abstract. In this paper, consistency of fuzzy relational equations involving k-regular block fuzzy matrices is discussed. Solutions of xM=b, where M is a block fuzzy matrix whose diagonal blocks are k-regular are ...
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Gradient projection method with a new step size for the split feasibility problem
... Both the CQ algorithm and the relaxed CQ algorithm used a fixed step size related to the largest eigenvalue of the matrix A ∗ A or the spectral radius of the self-adjoint operator A ∗ A, which sometimes affects convergence ...
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On the relation between Moore's and Penrose's conditions
... 3. Comment and examples. Most research publications in the area of generalized inversion adopt Penrose’s definition of four conditions, and overlook Moore’s defini- tion of three conditions. If Moore’s unique ...
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A New Method for Computing the Inverses of Anti-Tridiagonal and Anti-Pentadiagonal Matrices
... In this section, we give an approach to compute the inverses of ant-tridiagonal and ant- pentadiagonal matrices. We always assume that matrices discussed are nonsingular, unless otherwise stated. Suppose that and ...
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A Rapid Numerical Algorithm to Compute Matrix Inversion
... approximate inverses of the matrix A is to use iteration- type methods for this purpose which are based on matrix multiplications and are of great interest and accuracy when implementing on parallel ...
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2. Stability of a linear integro-differential equation of first order with variable delays
... [1] Ardjouni, A., Djoudi, A., Stability in nonlinear neutral integro-differential equations with variable delay using fixed point theory.. A., Stability, fixed points and inverses of del[r] ...
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On testing for the mean vector of a multivariate distribution with generalized and {2} inverses
... When the ovarian e matrix was singular or approximately singular, and when the alternative lied in the eigenspa e asso iated to the non-null eigenvalues, test statisti s based on f2g-inv[r] ...
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Efficient and Secure Delegation of Group Exponentiation to a Single Server
... group inverses, where both security and privacy hold against a computationally unrestricted, malicious, ...for inverses works for any (even non- commutative) group, only requires the client to perform 3 ...
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