[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14317/jami.2015.247

EXPLICIT MINIMUM POLYNOMIAL, EIGENVECTOR AND INVERSE FORMULA OF DOUBLY LESLIE MATRIX

WANICHARPICHAT, WIWAT (Department of Mathematics, Faculty of Science, Naresuan University)

Publication Information

Journal of applied mathematics & informatics / v.33, no.3_4, 2015 , pp. 247-260 More about this Journal

Abstract

The special form of Schur complement is extended to have a Schur's formula to obtains the explicit formula of determinant, inverse, and eigenvector formula of the doubly Leslie matrix which is the generalized forms of the Leslie matrix. It is also a generalized form of the doubly companion matrix, and the companion matrix, respectively. The doubly Leslie matrix is a nonderogatory matrix.

Keywords

Schur complement; Leslie matrix; doubly Leslie matrix; companion matrix; Toeplitz matrix; nonderogatory matrix; eigenvalue; eigenvector;

Citations & Related Records

Reference

1	W. Wanicharpichat, Explicit eigenvectors formulae for lower doubly companion matrices, Thai J. Math., 11(2) (2013), 261-274.
2	F. Zhang, The Schur Complement and Its Applications, in Series: Numerical Methods and Algorithms, Springer, Inc., New York, 2005.
3	C. Brezinski, Other Manifestations of the Schur Complement, Linear Algebra Appl., 111 (1988) 231-247. DOI
4	J.C. Butcher and P. Chartier, The effective order of singly-implicit Runge-Kutta methods, Numerical Algorithms, 20 (1999), 269-284. DOI
5	M.Q. Chen and X. Li, Spectral properties of a near-periodic row-stochastic Leslie matrix, Linear Algebra Appl., 409 (2005), 166-186. DOI
6	R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1996.
7	S.J. Kirkland and M. Neumann, Convexity and concavity of the Perron root and vector of Leslie matrices with applications to a population model, SIAM J. Matrix Anal. Appl., 15(4) (1994), 1092-1107. DOI
8	P. Lancaster and M. Tismenetsky, The Theory of Matrices Second Edition with Applications, Academic Press Inc., San Diego, 1985.
9	C.D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, Philadelphia, 2000.
10	S. Moritsugu and K. Kuriyama, A linear algebra method for solving systems of algebraic equations, J. Jap. Soc. Symb. Alg. Comp. (J. JSSAC), 7/4 (2000), 2-22.
11	N. Bacaër, A Short History of Mathematical Population Dynamics, Springer, New York, 2011.
12	L. Brand, The companion matrix and its properties, The American Mathematical Monthly, 71(6) (1964) 629-634. DOI
13	D. Poole, Linear Algebra: A Modern Introduction, Second Edition, Thomson Learning, London, 2006.
14	W. Wanicharpichat, Nonderogatory of sum and product of doubly companion matrices, Thai J. Math., 9(2) (2011), 337-348.