An extended operator trigonometry

Linear Algebra and Its Applications

Volumn 319, Issue 1-3, 2000, Pages 117-135

  Gustafson, Karl ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

Antieigenvalue; Invertible matrices; Operator trigonometry

Indexed keywords

EID: 0034369378     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(00)00170-1     Document Type: Article

References (30)

1. K. Gustafson, Lectures on Computational Fluid Dynamics, Mathematical Physics, and Linear Algebra, Kaigai Publications, Tokyo, 1996; World Scientific, Singapore, 1997.
2. K. Gustafson, D. Rao, Numerical Range: The Field of Values of of Linear Operators and Matrices, Springer, New York, 1997.
3. Gustafson K. A note on left multiplication of semigroup generators. Pacific J. Math. 24:1968;463-465.
4. Gustafson K. A min-max theorem. Notices Amer. Math. Soc. 15:1968;799.
5. K. Gustafson, Antieigenvalue inequalities in operator theory, in: O. Shisha (Ed.), Inequalities III, Los Angeles, 1969; Academic Press, New York, 1972, pp. 115-119.
6. K. Gustafson, Antieigenvalues in analysis, in: C. Stanojevic, O. Hadzic (Eds.), Proceedings of the Fourth International Workshop in Analysis and its Applications, Dubrovnik, 1990; Novi Sad, Yugoslavia, 1991, pp. 57-69.
7. Gustafson K. Positive (noncommuting) operator products and semigroups. Math. Z. 105:1968;160-172.
8. K. Gustafson, Trigonometric interpretation of iterative methods, in: O. Axelsson, B. Polman (Eds.), Proceedings of the Conference on Algebraic Multilevel Iteration Methods with Applications, Nijmegen, The Netherlands, 1996, pp. 23-29.
9. Gustafson K. Operator trigonometry. Linear and Multilinear Algebra. 37:1994;139-159.
10. Gustafson K., Antieigenvalues Linear Algebra Appl. 208/209:1994;437-454.
11. Gustafson K. Matrix trigonometry. Linear Algebra Appl. 217:1995;117-140.
12. Gustafson K. Operator trigonometry of iterative methods. Numer. Linear Algebra Appl. 4:1997;333-347.
13. Gustafson K. Domain decomposition, operator trigonometry. Robin Condition, Contemp. Math. 218:1998;455-460.
14. Gustafson K. Operator trigonometry of the model problem. Numer. Linear Algebra Appl. 5:1998;377-399.
15. K. Gustafson, Commentary on topics in the analytic theory of matrices, Section 23, Singular angles of a square matrix, in: B. Huppert, H. Schneider (Eds.), Collected Works of Helmut Wielandt 2, De Gruyters, Berlin, 1996, pp. 356-367.
16. K. Gustafson, The operator trigonometry of statistical efficiency, to appear.
17. K. Gustafson, Partial Differential Equation and Hilbert Space Methods, third ed., Revised, Dover, New York, 1999.
18. Watson G.S., Alpargu G., Styan G.P.H. Some comments on six inequalities associated with the inefficiency of ordinary least squares with one regressor. Linear Algebra Appl. 264:1997;13-54.
19. R. Horn, C. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1990.
20. Gustafson K. The geometrical meaning of the Kantorovich-Wielandt inequalities. Linear Algebra Appl. 296:1999;143-151.
21. O. Axelsson, Iterative Solution Methods, Cambridge University Press, Cambridge, 1994.
22. Gustafson K. State diagrams for Hilbert space operators. J. Math. Mech. 18:1968;33-46.
23. Gustafson K. Operator spectral states. Comput. Math. Appl. 34:1997;467-508.
24. Davis C. Extending the Kantorovich inequalities to normal matrices. Linear Algebra Appl. 31:1980;173-177.
25. Mirman B. Antieigenvalues: method of estimation and calculation. Linear Algebra Appl. 49:1983;247-255.
26. Gustafson K., Seddighin M. Antieigenvalue bounds. J. Math. Anal. Appl. 143:1989;327-340.
27. Gustafson K., Seddighin M. A note on total antieigenvectors. J. Math. Anal. Appl. 178:1993;603-611.
28. T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1980.
29. G. Golub, C. Van Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, MD, 1989.
30. Gustafson K., Zwahlen B. On the cosine of unbounded operators. Acta Sci. Math. 30:1969;33-34.