DAVID H. CARLSON
TTh, 11:00-12:20, 3:30-4:20, and by appointment
A.B. San Diego State College 1957 Mathematics
M.S. University of Wisconsin-Madison 1959 Mathematics
Ph.D. University of Wisconsin-Madison 1963 Mathematics
Professional Positions Held:
HIGHLIGHTS, 1996 -
Graduate Theses Directed
OREGON STATE UNIVERSITY
1. Hill, Richard D., M.A. 1964. Generalizations of the Ostrowski-Schneider-Taussky Main Inertia Theorem.
2. Furcha, John A., M.A. 1966. A Study of Symmetric Matrices and Quadratic Forms Over Fields of Characteristic Two.
3. Hill, Richard D., Ph.D. 1968. Generalized Inertia Theory for Complex Matrices.
4. Green, Beryl M., Ph.D. 1969. Characterizations of Matrices for which certain determinental inequalities hold.
5. VanderBeek, John W., M.S. 1970.
SAN DIEGO STATE UNIVERSITY
1. Boley, Teresa, M.S. 1984. A Generalization of Random Walk and Ruin Problems.
2. Walker, Mark, M.S. 1984. D-stability of Acyclic Matrices.
3. Luna, Robert, M.S. 1991. Factorization of Polynomials over a Finite Field
Other Professional Activity:
SDSU ALUMNI AWARD FOR OUTSTANDING FACULTY CONTRIBUTION
LINEAR ALGEBRA AND ITS APPLICATIONS
LINEAR ALGEBRA CURRICULUM STUDY GROUP (LACSG)
AMERICAN MATHEMATICAL ASSOCIATION
SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS
ASSOCIATION OF OREGON FACULTIES, 1979-1982
OREGON INTERINSTITUTIONAL FACULTY SENATE, 1975-1977
Articles in refereed journals
1. Inertia theorems for matrices: the semi-definite case (with Hans Schneider). J. Math. Anal. Appl. 6 (1963) 430-446.
2. A note on M-matrix equations. J. Soc. Ind. Appl. Math. 11 (1963) 1027-1033.
3. A generalization of Cauchy's double alternant (with Chandler Davis). Can. Math. Bull. 7(1965) 273-278.
4. Rank and inertia bounds for matrices under R(AH) ≥ 0. J. Math. Anal. Appl. 10(1965) 100-111.
5. On real eigenvalues of complex matrices. Pac. J. Math. 15 (1965) 1119-1129.
6. A note on matrices over extension fields. Duke Math. J. 33(1966) 503-506.
7. Weakly sign-symmetric matrices and some determinantal inequalities. Colloq. Math. 17(1967) 123-129.
8. On some determinantal inequalities. Proc. AMS 19(1968) 462-466.
9. A new criterion for H-stability. Lin. Alg. Appl. 1 (1968) 59-64.
10. On extensions of Szasz's inequality. Archiv. der Math. XIX (1968) 167-170.
11. Inequalities relating the degrees of elementary divisors within a matrix. Simon Stevin,
12. Inequalities for the degrees of elementary divisors of modules. Lin. Alg. Appl. 5(1972) 293-298.
13. Minimal G-functions (with R.S. Varga). Lin. Alg. Appl. 6(1973) 97-117.
14. Minimal G-functions II (with R.S. Varga). Lin. Alg. Appl. 7(1973) 233-242.
15. On collections of G-functions (with R.S. Varga). Lin. Alg. Appl. 8(1974) 65-76.
16. A generalization of the Schur complement by means of the Moore-Penrose inverse (with Emilie Haynsworth and Thomas Markham). SIAM J. Appl. Math. 26(1974) 169-175.
17. A class of positive stable matrices. J. Res. NBS 78B (1974) 1-2.
18. Generalized inverse formulas using the Schur complement (with Fennell Burns, Emilie Haynsworth, and Thomas Markham). SIAM J. Appl. Math. 28(1975), 254-259.
19. On ranges of Lyapunov transformations (with Raphael Loewy). Lin. Alg. Appl. 8(1974) 237-248.
20. Matrix decompositions involving the Schur complement. SIAM J. Appl. Math. 28(1975) 577-587.
21. Cones of diagonally dominant matrices (with George Phillip Barker). Pac. J. Math. 57(1975) 15-32.
22. Generalizations of matrix monotonicity. Linear Alg. Appl. 13(1976) 125-131.
23. Generalized controllability and inertia theory (with R.D. Hill). Linear Alg. Appl. 15 (1976) 177-187.
24. Controllability and Inertia Theory for Functions of a Matrix (with R.D. Hill). Jour. Math. Anal. Appl. 59(1977) 260-266.
25. Schur complements of diagonally dominant matrices (with Thomas L. Markham). Czech. Math. J. 29 (104)(1979) 246-251.
26. The Lyapunov matrix equation SA + A*S = S*B*BS (with Biswa Nath Datta). Linear Alg. Appl. 28(1979) 43-52.
27. On the effective computation of the inertia of a non-hermitian matrix (with Biswa Nath Datta). Numer. Math. 33(1979) 315-322.
28. Induced bilinear maps and matrix equations (with Raphael Loewy). Lin. Multilin. Alg. 9(1980) 17-33.
29. Generalizations of top heavy cones (with George Phillip Barker). Lin. Multilin. Alg. 8(1980) 43-54.
30. On equality of maps induced by alternate products (with Raphael Loewy). Lin.Alg. Appl. 47(1982) 89-110.
31. A semidefinite Lyapunov theorem and the characterization of tridiagonal D-stable matrices (with B.N. Datta and C.R. Johnson). SIAM Jour. Alg. Disc. Meth. 3(1982) 293-304.
32. Minimax and interlacing theorems for matrices. Lin. Alg. Appl. Reports 54(1983) 153- 172.
33. Complementable and almost definite matrices (with E.V. Haynsworth). Linear Alg. Appl. 52-53 (1983) 157-176.
34. Controllability, inertia, and stability for tridiagonal matrices. Linear Alg. Appl. 56(1984)
35. Generalized minimax and interlacing theorems (with E. Marques de Sa'). Lin. Multilin. Alg. 15(1984) 77-103.
36. On the controllability of matrix pairs (A,K) with K positive semidefinite (with B. N. Datta and Hans Schneider). SIAM J. Alg. Disc. Meth. 5 (1984) 346-350.
37. On equality of maps induced by tensor and symmetric products (with Raphael Loewy). Lin. Multilin. Alg. 47(1982) 89-110.
38. Common eigenvectors and quasi-commutativity (with Stephen Pierce). Lin. Alg. Appl. 71(1985) 49-55.
39. What are Schur complements, anyway? Linear Alg. Appl. Reports. 74(1986) 257-275.
40. Nonsingularity criteria for matrices involving combinatorial considerations. Lin. Alg. Appl. 107(1988) 41-56.
41. Nonsingularity criteria for general combinatorially symmetric matrices (with Daniel Hershkowitz). Lin. Alg. Appl. 114/115 (1989) 399-416.
42. Block diagonal semistability factors and Lyapunov semistability of block triangular matrices (with Daniel Hershkowitz and Dafna Shasha). Lin. Alg. Appl. 172 (1992) 1- 25.
43. On the controllability of matrix pairs (A,K) with K positive semidefinite. II. SIAM J. Matrix Anal is 15 (1994) 129-133.
44. Extremal patterns of distinct entries in the range of a matrix (with Charles R. Johnson). Lin. Multilin. Alg. 43(1997) 283-297.
Article in refereed proceedings
1. Generalized inverse invariance, partial orders, and rank-minimization problems for matrices, p. 81-87 in Current Trends in Matrix Theory (Frank Uhlig and Robert Grone, Eds.) North-Holland, New York, 1987.
1. Linear Algebra and its Role in Systems Theory (with Richard Brualdi, Biswa Datta, Charles Johnson, and Robert Plemmons). Amer. Math. Society, Contemporary Mathematics Series, Volume 47, Providence, 1985.
Articles in refereed journals
1. Gems of exposition in elementary linear algebra (with Charles R. Johnson, David Lay, and A. Duane Porter). College Mathematics Journal 23 (1992) 299-303.
2. Teaching linear algebra: must the fog always roll in? College Mathematics Journal 24 (1993) 29-40.
3. The Linear Algebra Curriculum Study Group recommendations for the first course in linear algebra (with Charles R. Johnson, David C. Lay, and A. Duane Porter). College Mathematics Journal 24 (1993) 41-46.
Article in refereed proceedings
1. Recent developments in the teaching of linear algebra in the United States, Aportaciones Mathematicas 14 (1994) 371-382.
Other articles on teaching practice
1. Linear algebra curriculum reform: a progress report. SIAM News, May 1993, p.22; reprinted in You’re the Professor, What Next? (Bettye Anne Case, Editor). Math. Assoc. Amer. Notes, Volume 35, Washington, D.C., 1994.
2. Changing calculus: its impact on the post-calculus curriculum (with Wayne Roberts), p. 149-151 in Calculus: The Dynamics of Change (Wayne Roberts, Editor), Math. Assoc. Amer. Notes, Volume 39, Washington, D.C., 1996.
3. Response to Linear Algebra in the Core I, p. 67-68 in Confronting the Core Curriculum
(John Dossey, Editor), Math. Assoc. Amer. Notes, Volume 45, Washington, D.C., 1998.
4. Report on the Educational Program at the Hans Schneider Linear Algebra Conference,
Madison, Wisconsin, June 3-6, 1998 (with Frank Uhlig), Linear Algebra and Its
Applications, 302-303 (1999) 615-617.
5. Eigenvectors are nonzero vectors scaled by a linear map, Image (The Bulletin of the
International Linear Algebra Society), 25 (2001) 32.
1. Resources for Teaching Linear Algebra (with Charles R. Johnson, David C. Lay, A. Duane Porter, Ann Watkins, and William Watkins). Math. Assoc. Amer. Notes, Volume 42, Washington, D.C., 1997.
2. Linear Algebra Gems: Assets for Undergraduate Mathematics (with Charles R. Johnson, David C. Lay, and A. Duane Porter). Math. Assoc. Amer. Notes, Washington, D.C., to appear.
Other Professional Articles
1. Emilie Haynsworth, 1916-1985 (with Thomas Markham and Frank Uhlig). Linear Alg. Appl. Reports. 75(1986) 269-276.
2. Linear algebra curriculum reform. SIAM News, November, 1991, p. 10.
3. Linear algebra at SIAM. UME Trends, January, 1992, p.7.
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