Solution to a Class of Matrix Equations with k-Involutary Symmetrices

Abstract:

In this paper, we investigate the solvability of matrix equations with -involutary symmetric matrix , the general solution of which is obtained when it is solvable. Meantime, the associated optimal approximation problem for some given matrix is also considered under some particular hypothesis.

Info:

Periodical:

Advanced Materials Research (Volumes 457-458)

Main Theme:

Edited by:

Sally Gao

Pages:

799-803

DOI:

10.4028/www.scientific.net/AMR.457-458.799

Citation:

M. L. Liang and L. F. Dai, "Solution to a Class of Matrix Equations with k-Involutary Symmetrices", Advanced Materials Research, Vols. 457-458, pp. 799-803, 2012

Online since:

January 2012

Authors:

Export:

Price:

\$35.00

Permissions:

[1] I.J. Good: The inverse of a centro-symmetric matrix, Tech-nometrics, vol. 12 (1970), pp.153-156.

[2] A.L. Andrew: Solution of equations involving centrosymmetric matrices, Technometrics, vol. 15, (1973), pp.405-407.

DOI: 10.2307/1266998

[3] I.S. Pressman: Matrices with multiple symmetry properties: applications of centrohermitian and perhermitian matrices, Linear Algebra Appl., vol. 284 (1998), pp.239-258.

DOI: 10.1016/s0024-3795(98)10144-1

[4] Z. Xu, K.Y. Zhang, Q. Lu: Fast Algorithms of TOEPLITZ Form, Northwest Industry Univ. Press, (1999).

[5] A.P. Liao, Y. Lei: Least-squares solutions of matrix inverse problem for bi-symmetric matrices with a submatrix constraint, Numer. Linear Algebra Appl.,. vol. 14(5) (2007), pp.425-444.

DOI: 10.1002/nla.530

[6] D.X. Xie, L. Zhang, X.Y. Hu: The solvability conditions for the inverse problem of bisymmetric nonnegative definite matrices, J. Comput. Math., vol. 6 (2000), pp.597-608.

[7] H.C. Chen: Generalized reflexive matrices: special properties and applications, Matrix Anal. Appl., vol. 19 (1998), pp.140-153.

[8] W.F. Trench: Characterization and properties of matrices with generalized symmetry or skew symmetry, Linear Algebra Appl., vol. 377 (2004), pp.207-218.

DOI: 10.1016/j.laa.2003.07.013

[9] Y.X. Yuan, H. Dai: Generalized reflexive solutions of the matrix equation AXB=D and an associated optimal approximation problem, Comput. Math. Appl., vol. 56 (2008), pp.1643-1649.

[10] W.F. Trench: Minimization problems for (R, S)-symmetric and (R, S)-skew symmetric matrices, Linear Algebra Appl., vol. 389 (2004), pp.23-31.

DOI: 10.1016/j.laa.2004.03.035

[11] W.F. Trench: Characterization and properties of matrices with k-involutory symmetries, Linear Algebra Appl., vol. 429 (2010), pp.2278-2290.

DOI: 10.1016/j.laa.2008.07.002

[12] W.F. Trench: Characterization and properties of matrices with k-involutory symmetries II. Linear Algebra Appl., vol. 432 (2010), pp.2782-2797.

[13] H.C. Chen, A. Sameh: A matrix decomposition method for orthotropic elasticity problems, SIAM J. Matrix Anal. Appl., vol. 10 (1989), pp.39-64.

DOI: 10.1137/0610004

[14] Z.G. Jia, Q. Wang, M.S. Wei: Procrustes problems for (P, Q, \eta)-reflexive matrices, J. Comput. Appl. Math., vol. 233 (2010), pp.3041-3045.

[15] L. Zhang, D.X. Xie: A class of inverse eigenvalue problems, Math. Sci. Acta, vol. 13 (1993), pp.94-99.

In order to see related information, you need to Login.