DAVID H. CARLSON

Office Hours: 
TTh, 11:0012:20, 3:304:20, and by appointment 
Current Courses: 
Fall, 2001
Spring 2002

Education: 
A.B. San Diego State College 1957 Mathematics M.S. University of WisconsinMadison 1959 Mathematics Ph.D. University of WisconsinMadison 1963 Mathematics 
Professional Positions Held: 

HIGHLIGHTS, 1996  

Graduate Theses Directed 
OREGON STATE UNIVERSITY 1. Hill, Richard D., M.A. 1964. Generalizations of the OstrowskiSchneiderTaussky 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. Dstability 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, 19791982
OREGON INTERINSTITUTIONAL FACULTY SENATE, 19751977

Mathematics Research 
Articles in refereed journals 1. Inertia theorems for matrices: the semidefinite case (with Hans Schneider). J. Math. Anal. Appl. 6 (1963) 430446. 2. A note on Mmatrix equations. J. Soc. Ind. Appl. Math. 11 (1963) 10271033. 3. A generalization of Cauchy's double alternant (with Chandler Davis). Can. Math. Bull. 7(1965) 273278. 4. Rank and inertia bounds for matrices under R(AH) ≥ 0. J. Math. Anal. Appl. 10(1965) 100111. 5. On real eigenvalues of complex matrices. Pac. J. Math. 15 (1965) 11191129. 6. A note on matrices over extension fields. Duke Math. J. 33(1966) 503506. 7. Weakly signsymmetric matrices and some determinantal inequalities. Colloq. Math. 17(1967) 123129. 8. On some determinantal inequalities. Proc. AMS 19(1968) 462466. 9. A new criterion for Hstability. Lin. Alg. Appl. 1 (1968) 5964. 10. On extensions of Szasz's inequality. Archiv. der Math. XIX (1968) 167170. 11. Inequalities relating the degrees of elementary divisors within a matrix. Simon Stevin, 44(1970) 310. 12. Inequalities for the degrees of elementary divisors of modules. Lin. Alg. Appl. 5(1972) 293298. 13. Minimal Gfunctions (with R.S. Varga). Lin. Alg. Appl. 6(1973) 97117. 14. Minimal Gfunctions II (with R.S. Varga). Lin. Alg. Appl. 7(1973) 233242. 15. On collections of Gfunctions (with R.S. Varga). Lin. Alg. Appl. 8(1974) 6576. 16. A generalization of the Schur complement by means of the MoorePenrose inverse (with Emilie Haynsworth and Thomas Markham). SIAM J. Appl. Math. 26(1974) 169175. 17. A class of positive stable matrices. J. Res. NBS 78B (1974) 12. 18. Generalized inverse formulas using the Schur complement (with Fennell Burns, Emilie Haynsworth, and Thomas Markham). SIAM J. Appl. Math. 28(1975), 254259. 19. On ranges of Lyapunov transformations (with Raphael Loewy). Lin. Alg. Appl. 8(1974) 237248. 20. Matrix decompositions involving the Schur complement. SIAM J. Appl. Math. 28(1975) 577587. 21. Cones of diagonally dominant matrices (with George Phillip Barker). Pac. J. Math. 57(1975) 1532. 22. Generalizations of matrix monotonicity. Linear Alg. Appl. 13(1976) 125131. 23. Generalized controllability and inertia theory (with R.D. Hill). Linear Alg. Appl. 15 (1976) 177187. 24. Controllability and Inertia Theory for Functions of a Matrix (with R.D. Hill). Jour. Math. Anal. Appl. 59(1977) 260266. 25. Schur complements of diagonally dominant matrices (with Thomas L. Markham). Czech. Math. J. 29 (104)(1979) 246251. 26. The Lyapunov matrix equation SA + A*S = S*B*BS (with Biswa Nath Datta). Linear Alg. Appl. 28(1979) 4352. 27. On the effective computation of the inertia of a nonhermitian matrix (with Biswa Nath Datta). Numer. Math. 33(1979) 315322. 28. Induced bilinear maps and matrix equations (with Raphael Loewy). Lin. Multilin. Alg. 9(1980) 1733. 29. Generalizations of top heavy cones (with George Phillip Barker). Lin. Multilin. Alg. 8(1980) 4354. 30. On equality of maps induced by alternate products (with Raphael Loewy). Lin.Alg. Appl. 47(1982) 89110. 31. A semidefinite Lyapunov theorem and the characterization of tridiagonal Dstable matrices (with B.N. Datta and C.R. Johnson). SIAM Jour. Alg. Disc. Meth. 3(1982) 293304. 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. 5253 (1983) 157176. 34. Controllability, inertia, and stability for tridiagonal matrices. Linear Alg. Appl. 56(1984) 207220. 35. Generalized minimax and interlacing theorems (with E. Marques de Sa'). Lin. Multilin. Alg. 15(1984) 77103. 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) 346350. 37. On equality of maps induced by tensor and symmetric products (with Raphael Loewy). Lin. Multilin. Alg. 47(1982) 89110. 38. Common eigenvectors and quasicommutativity (with Stephen Pierce). Lin. Alg. Appl. 71(1985) 4955. 39. What are Schur complements, anyway? Linear Alg. Appl. Reports. 74(1986) 257275. 40. Nonsingularity criteria for matrices involving combinatorial considerations. Lin. Alg. Appl. 107(1988) 4156. 41. Nonsingularity criteria for general combinatorially symmetric matrices (with Daniel Hershkowitz). Lin. Alg. Appl. 114/115 (1989) 399416. 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) 129133. 44. Extremal patterns of distinct entries in the range of a matrix (with Charles R. Johnson). Lin. Multilin. Alg. 43(1997) 283297. Article in refereed proceedings 1. Generalized inverse invariance, partial orders, and rankminimization problems for matrices, p. 8187 in Current Trends in Matrix Theory (Frank Uhlig and Robert Grone, Eds.) NorthHolland, New York, 1987. Book edited 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. 
Teaching Practice 
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) 299303. 2. Teaching linear algebra: must the fog always roll in? College Mathematics Journal 24 (1993) 2940. 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) 4146. Article in refereed proceedings 1. Recent developments in the teaching of linear algebra in the United States, Aportaciones Mathematicas 14 (1994) 371382. 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 postcalculus curriculum (with Wayne Roberts), p. 149151 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. 6768 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 36, 1998 (with Frank Uhlig), Linear Algebra and Its Applications, 302303 (1999) 615617. 5. Eigenvectors are nonzero vectors scaled by a linear map, Image (The Bulletin of the International Linear Algebra Society), 25 (2001) 32. Books edited 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, 19161985 (with Thomas Markham and Frank Uhlig). Linear Alg. Appl. Reports. 75(1986) 269276. 2. Linear algebra curriculum reform. SIAM News, November, 1991, p. 10. 3. Linear algebra at SIAM. UME Trends, January, 1992, p.7. 
Hobbies 
travel, ushering plays and classical music, jogging and swimming 
The information on personal home pages represents that of the author and not necessarily that of San Diego State University. The author takes full responsibility for the information presented.
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