×

Maximal invariant neutral subspaces and an application to the algebraic Riccati equation. (English) Zbl 0521.15017


MSC:

15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
15A24 Matrix equations and identities
47A15 Invariant subspaces of linear operators
47B25 Linear symmetric and selfadjoint operators (unbounded)
47B50 Linear operators on spaces with an indefinite metric
15B57 Hermitian, skew-Hermitian, and related matrices
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] BOGNAR,J.: Indefinite inner product spaces. New York-Heidelberg-Berlin, Springer 1974. · Zbl 0286.46028
[2] COPPEL, W.A.: Matrix quadratic equations. Bull. Austral. Math. Soc.10, 377-401 (1974). · Zbl 0276.15019 · doi:10.1017/S0004972700041071
[3] GOHBERG, I., LANCASTER, P., & RODMAN, L.: Spectral analysis of selfadjoint matrix polynomials. Res. Paper No. 419, Dept. of Mathematics and Statistics, University of Calgary, Canada (1979). · Zbl 0424.47010
[4] GOHBERG, I., LANCASTER, P., & RODMAN, L.: Perturbations of H-selfadjoint matrices with applications to differential equations. To appear in Integral Equations and Operator Theory. · Zbl 0511.15010
[5] GOHBERG, I., LANCASTER, P., & RODMAN, L.: Matrix polynomials. To appear in Academic Press.
[6] HUA, L.K.: On the theory of automorphic functions of a matrix variable, II. The classification of hypercircles under the symplectic group. Amer. J. Math.66, 531-563 (1944). · Zbl 0063.02921 · doi:10.2307/2371765
[7] LANCASTER, P., RODMAN, L.: Existence and uniqueness theorems for the algebraic Riccati equation. Int. J. Control32, 285-309 (1980). · Zbl 0439.49011 · doi:10.1080/00207178008922858
[8] MAL’LEV, A.I.: Foundations of Linear Algebra. San Francisco-London, W.H. Freeman 1963.
[9] MARTENSSON, K.: On the matrix Riccati equation. Information Sciences3, 17-49 (1971). · Zbl 0206.45602 · doi:10.1016/S0020-0255(71)80020-8
[10] POTTER, J.E.: Matrix quadratic solutions. J. SIAM Appl. Math.14, 496-501 (1966). · Zbl 0144.02001 · doi:10.1137/0114044
[11] SHAYMAN, M.A.: Classification theorems for the algebraic Riccati equation: a synthesis. International Symposium on Mathematical Theory of Networks and Systems4, 257-261 (1981).
[12] SHAYMAN, M.A.: Geometry of the algebraic Riccati equation. In preparation. · Zbl 0537.93022
[13] WILLEMS, J.C.: Least Squares Stationary Optimal Control and the Algebraic Riccati Equation. IEEE Trans. on Aut. Cont.AC-16, 621-634 (1971). · doi:10.1109/TAC.1971.1099831
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.