How to establish universal block-matrix factorizations

Electronic Journal of Linear Algebra

Volumn 8, Issue , 2001, Pages 115-127

  Tian, Yongge ^a   Styan, George P H ^b  

^a QUEEN S UNIVERSITY   (Canada)

^b MCGILL UNIVERSITY   (Canada)

Author keywords

Block matrix; Determinant; Idempotent matrices; Involutory matrices; Quaternion matrices; Universal factorization

Indexed keywords

EID: 3042523493     PISSN: 10813810     EISSN: None     Source Type: Journal    
DOI: 10.13001/1081-3810.1065     Document Type: Article

References (12)

1. H. Aslaksen, Quaternionic determinants, Math. Intelligencer, 18:57-65, 1996.
2. N. Cohen and S. De Leo, The quaternionic determinant, Electronic J. Linear Algebra, 7:100-111, 2000.
3. P. J. Davis, Circulant Matrices, Second Edition, AMS Chelsea Publishing, New York, 1994.
4. W. R. Ferng, K.-Y. Lin and W.-W. Lin, A novel nonsymmetric K _-Lanczos algorithm for the generalized nonsymmetric K _-eigenvalue problems, Linear Algebra Appl., 252:81-105, 1997.
5. G. N. Hile and P. Lounesto, Matrix representations of Clifford algebras, Linear Algebra Appl., 128:51-63, 1990.
6. R. A. Horn and C. R. Johnson, Matrix Analysis, Corrected Reprint Edition, Cambridge University Press, 1990,
7. T. Y. Lam, The Algebraic Theory of Quadratic Forms, Second printing, with revisions. Mathematics Lecture Notes Series vol. 54, The Benjamin/Cummings Publishing Company, Reading, Mass., 1980.
8. R. S. Pierce, Associative Algebras, Springer, New York, 1982.
9. I. R. Porteous, Clifford Algebras and the Classical Groups, Cambridge Studies in Advanced Mathematics vol. 50, Cambridge University Press, 1995.
10. Y. Tian, Universal similarity factorization equalities over real Clifford algebras, Adv. Appl. Clifford Algebras, 8:365-402, 1998.
11. Y. Tian, Universal factorization equalities for quaternion matrices and their applications, Math. J. Okayama Univ., 42:45-62, 1999.
12. Y. Tian, Universal similarity equalities over complex Clifford algebras, in Clifford Algebras and Their Applications in Mathematical Physics: Proceedings of the Fifth Conference, Ixtapa-Zihuatanejo, Mexico, June 27-July 4, 1999, Volume 1: Algebra and Physics, R. Ablstrok;amowicz, B. Fauser, eds., Progress in Physics vol. 18, Birkhäuser, Boston, pp. 435-448, 2000.