Stability of Invariant Subspaces of Quaternion Matrices

被引：6

作者：

Rodman, Leiba ^{[1
]}

机构：

[1] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2012年 / 6卷 / 05期

关键词：

Quaternion matrix; Invariant subspace; Matrix equation; FINITE-DIMENSIONAL POINTS; PERTURBATION-THEORY; CONTINUITY; DISTANCE;

D O I：

10.1007/s11785-012-0233-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A quaternion invariant subspace of a quaternion matrix is said to be stable (in the sense of robustness) if every nearby matrix has an invariant subspace close to the original one. Under mild hypothesis, necessary and sufficient conditions are given for quaternion invariant subspaces to be stable. Other notions of stability of quaternion invariant subspaces are studied as well, and stability criteria developed. Applications to robustness of solutions of certain classes of quaternion matrix equations are given.

引用

页码：1069 / 1119

页数：51

共 50 条

[41] Rational Procedures in the Problem of Common Invariant Subspaces of Two Matrices
Yu. A. Al'pin
Kh. D. Ikramov
[J]. Journal of Mathematical Sciences, 2003, 114 (6) : 1757 - 1764
[42] Simple forms and invariant subspaces of H-expansive matrices
Fourie, J. H.
Groenewald, G. J.
van Rensburg, D. B. Janse
Ran, A. C. M.
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 470 : 300 - 340
[43] Hyponormal matrices and semidefinite invariant subspaces in indefinite inner products
Mehl, C
Ran, ACM
Rodman, L
[J]. ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2004, 11 : 192 - 204
[44] NONSINGULAR FACTORS OF POLYNOMIAL-MATRICES AND (A,B)-INVARIANT SUBSPACES
EMRE, E
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1980, 18 (03) : 288 - 296
[45] On a functional approach to constructing projections onto invariant subspaces of matrices
Demidenko, GV
[J]. SIBERIAN MATHEMATICAL JOURNAL, 1998, 39 (04) : 683 - 699
[46] On a functional approach to constructing projections onto invariant subspaces of matrices
G. V. Demidenko
[J]. Siberian Mathematical Journal, 1998, 39 : 683 - 699
[47] An overview of relative sin Θ theorems for invariant subspaces of complex matrices
Ipsen, ICF
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 123 (1-2) : 131 - 153
[48] The Riccati algorithm for eigenvalues and invariant subspaces of matrices with inexpensive action
Brandts, J
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 358 : 335 - 365
[49] FAST PARALLELIZABLE METHODS FOR COMPUTING INVARIANT SUBSPACES OF HERMITIAN MATRICES
Zhenyue Zhang Department of Mathematics
[J]. Journal of Computational Mathematics, 2007, (05) : 583 - 594
[50] Subscalarity, Invariant, and Hyperinvariant Subspaces for Upper Triangular Operator Matrices
Mecheri, Salah
[J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2018, 41 (02) : 1085 - 1104

← 1 2 3 4 5 →