• Title/Summary/Keyword: inverse matrices

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THE MOORE-PENROSE INVERSE OF THE PARTITIONED MARIX AND SIMULATION STUDY

  • Sunwoo, Ha-Sik
    • Journal of applied mathematics & informatics
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    • v.5 no.3
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    • pp.849-857
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    • 1998
  • In this paper we have a concern on the Moore-Penrose inverse of two kinds of partitioned matrices of the form [V X] and [{{{{ {V atop {X} {{{{ {X atop { 0} }}] where V is symmetric. The Moore-Penrose inverse of the partitioned matrices can be reduced to be simpler forms according to some algebraic conditions. Firstly we investigate the representations of the Moore-Penrose inverses of the partitioned matrices under four al-gebraic conditions. Each condition reduces the Moore-Penrose inverses of the partitioned matrices under four al-gebraic conditions. Each condition reduces the Morre-Penrose inverse into some simpler form. Also equivalant conditions will be considered. Finally we will perform a simulation study to investigate which con-dition is the most important in the sense that which condition occurs the most frequently in the real situation. The simluation study will show us a particular condition occurs the most likely tha other conditions. This fact enables us to obtain the Morre-Penrose inverse with less computational efforts and computational storage.

THE SOLVABILITY CONDITIONS FOR A CLASS OF CONSTRAINED INVERSE EIGENVALUE PROBLEM OF ANTISYMMETRIC MATRICES

  • PAN XIAO-PING;HU XI-YAN;ZHANG LEI
    • Journal of the Korean Mathematical Society
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    • v.43 no.1
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    • pp.87-98
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    • 2006
  • In this paper, a class of constrained inverse eigenvalue problem for antisymmetric matrices and their optimal approximation problem are considered. Some sufficient and necessary conditions of the solvability for the inverse eigenvalue problem are given. A general representation of the solution is presented for a solvable case. Furthermore, an expression of the solution for the optimal approximation problem is given.

NONNEGATIVE INTEGRAL MATRICES HAVING GENERALIZED INVERSES

  • Kang, Kyung-Tae;Beasley, LeRoy B.;Encinas, Luis Hernandez;Song, Seok-Zun
    • Communications of the Korean Mathematical Society
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    • v.29 no.2
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    • pp.227-237
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    • 2014
  • For an $m{\times}n$ nonnegative integral matrix A, a generalized inverse of A is an $n{\times}m$ nonnegative integral matrix G satisfying AGA = A. In this paper, we characterize nonnegative integral matrices having generalized inverses using the structure of nonnegative integral idempotent matrices. We also define a space decomposition of a nonnegative integral matrix, and prove that a nonnegative integral matrix has a generalized inverse if and only if it has a space decomposition. Using this decomposition, we characterize nonnegative integral matrices having reflexive generalized inverses. And we obtain conditions to have various types of generalized inverses.

COMPUTING GENERALIZED INVERSES OF A RATIONAL MATRIX AND APPLICATIONS

  • Stanimirovic, Predrag S.;Karampetakis, N. P.;Tasic, Milan B.
    • Journal of applied mathematics & informatics
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    • v.24 no.1_2
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    • pp.81-94
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    • 2007
  • In this paper we investigate symbolic implementation of two modifications of the Leverrier-Faddeev algorithm, which are applicable in computation of the Moore-Penrose and the Drazin inverse of rational matrices. We introduce an algorithm for computation of the Drazin inverse of rational matrices. This algorithm represents an extension of the papers [11] and [14]. and a continuation of the papers [15, 16]. The symbolic implementation of these algorithms in the package MATHEMATICA is developed. A few matrix equations are solved by means of the Drazin inverse and the Moore-Penrose inverse of rational matrices.

THE REPRESENTATION AND PERTURBATION OF THE W-WEIGHTED DRAZIN INVERSE

  • Xu, Zhaoliang;Wang, Guorong
    • Journal of applied mathematics & informatics
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    • v.23 no.1_2
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    • pp.113-126
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    • 2007
  • Let A and E be $m{\times}n$ matrices and W an $n{\times}m$ matrix, and let $A_{d,w}$ denote the W-weighted Drazin inverse of A. In this paper, a new representation of the W-weighted Drazin inverse of A is given. Some new properties for the W-weighted Drazin inverse $A_{d,w}\;and\;B_{d,w}$ are investigated, where B=A+E. In addition, the Banach-type perturbation theorem for the W-weighted Drazin inverse of A and B are established, and the perturbation bounds for ${\parallel}B_{d,w}{\parallel}\;and\;{\parallel}B_{d,w}-A_{d,w}{\parallel}/{\parallel}A_{d,w}{\parallel}$ are also presented. When A and B are square matrices and W is identity matrix, some known results in the literature related to the Drazin inverse and the group inverse are directly reduced by the results in this paper as special cases.

THE APPLICATIONS OF ADDITIVE MAP PRESERVING IDEMPOTENCE IN GENERALIZED INVERSE

  • Yao, Hongmei;Fan, Zhaobin;Tang, Jiapei
    • Journal of applied mathematics & informatics
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    • v.26 no.3_4
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    • pp.541-547
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    • 2008
  • Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with $n\;{\geq}\;3$. We denote by $M_n(R)$ the ring of all $n{\times}n$ matrices over R. Let ($J_n(R)$) be the additive subgroup of $M_n(R)$ generated additively by all idempotent matrices. Let ($D=J_n(R)$) or $M_n(R)$. In this paper, by using an additive idem potence-preserving result obtained by Coo (see [4]), I characterize (i) the additive preservers of tripotence from D to $M_m(R)$ when 2 and 3 are units of R; (ii) the additive preservers of inverses (respectively, Drazin inverses, group inverses, {1}-inverses, {2}-inverses, {1, 2}-inverses) from $M_n(R)$ to $M_n(R)$ when 2 and 3 are units of R.

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ON A FAST ITERATIVE METHOD FOR APPROXIMATE INVERSE OF MATRICES

  • Soleymani, Fazlollah
    • Communications of the Korean Mathematical Society
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    • v.28 no.2
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    • pp.407-418
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    • 2013
  • This paper studies a computational iterative method to find accurate approximations for the inverse of real or complex matrices. The analysis of convergence reveals that the method reaches seventh-order convergence. Numerical results including the comparison with different existing methods in the literature will also be considered to manifest its superiority in different types of problems.

LEVEL-m SCALED CIRCULANT FACTOR MATRICES OVER THE COMPLEX NUMBER FIELD AND THE QUATERNION DIVISION ALGEBRA

  • Jiang, Zhao-Lin;Liu, San-Yang
    • Journal of applied mathematics & informatics
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    • v.14 no.1_2
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    • pp.81-96
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    • 2004
  • The level-m scaled circulant factor matrix over the complex number field is introduced. Its diagonalization and spectral decomposition and representation are discussed. An explicit formula for the entries of the inverse of a level-m scaled circulant factor matrix is presented. Finally, an algorithm for finding the inverse of such matrices over the quaternion division algebra is given.