Professor of Mathematics

Phone Number: (619) 594-6670
Fax: (619) 594-6746
Office: BA-213
E-mail: carlson@math.sdsu.edu

Department of Mathematical and Computer Sciences
San Diego State University
5500 Campanile Drive
San Diego, CA 92182-7720

Office Hours:

TTh, 11:00-12:20, 3:30-4:20, and by appointment

Current Courses:

Fall, 2001

Spring 2002 

  • Math 121, Calculus for the Life Sciences, TTh 9:30-10:45, BA-346
  • Math 121, Calculus for the Life Sciences, TTh 2:00-3:15, BA-258


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:  

  • Univ. of Wisconsin-Madison 1957-1962 Graduate Teaching Assistant
  • Univ. of Wisconsin-Milwaukee 1962-1963 Instructor
  • Oregon State University 1963-1984 Asst. Professor to Professor
  • Universidad de la Republica, Uruguay 1965-1966 Fulbright Scholar
  • Kent State University 1970-1971 Visiting Professor
  • Universidade de Coimbra, Portugal 1977-1978 Visiting Professor
  • San Diego State University 1982-1984 Visiting Professor
  • 1984-1989 Chair
  • 1984- Professor
  • College of William and Mary 1994 Visiting Scholar



  • 1996-1997 Chair, MAA Program Committee for the 1997 Joint Mathematics Meetings
  • 1997 Principal Editor, Resources for Teaching Linear Algebra, MAA Notes, Vol. 42
  • 1999- Member, International Program Committee for a Study on the Future of the Teaching and Learning of Algebra sponsored by the International Commission on Mathematical Instruction
  • 2000 Sabbatical leave at University of Canterbury, Christchurch, NZ; University of Tasmania, Hobart; Melbourne University; Northern Territory University, Darwin; James Cook University, Townsville, Australia

Graduate Theses Directed


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.


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:

  • (College of Sciences) 1995.


  • Associate editor, 1971-1983
  • Advisory editor, 1984-
  • Special co-editor, 1976 Special Issue dedicated to Professor Olga Taussky-Todd
  • Special co-editor, 1991 Special Issue for the 1990 Auburn Conference
  • Special editor for educational papers, 1998 ILAS Conference Proceedings Issue


Formed in 1990 by David Carlson, Charles Johnson (William and Mary), David Lay (Maryland), and Duane Porter (Wyoming), to "initiate substantial and sustained national interest in improving the undergraduate linear algebra curriculum". Held NSF-funded Workshop in 1990 which developed recommendations which included a core course syllabus for the first course in linear algebra. Organized Special Sessions at the annual Joint Mathematics Meetings (1991-98). Compiled "Resources for Teaching Linear Algebra", MAA Notes, Volume 42. Compiled, with NSF support, a collection "Gems of Elementary Linear Algebra"; insightful proofs and expositions, and a variety of new problems and problem sets.


  • Member, Committee on Calculus reform and the First Two Years, 1991-1997


  • Chair, First Linear Algebra Prize Committee, 1987-88
  • Chair, Activity Group for Linear Algebra, 1989-91
  • Visiting Lecturer, 1992-


  • Vice-President 1979-1981.

The Association of Oregon Faculties is a voluntary dues-paying association of approximately 1000 faculty members in the Oregon State System of Higher Education. Its purpose is to provide lobbying support in the state legislative and executive branches for the faculty viewpoint in higher education. While Chairman of the Oregon Interinstitutional Faculty Senate in 1977, I authored a proposal for a faculty lobbying organization, which led to the formation of the Association of Oregon Faculties in 1979.


  • Chairman 1976-1977.

Mathematics Research

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,

44(1970) 3-10.

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.

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) 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.

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, 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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