ROBERT D. GRONE

Office Hours: 
TTh, 11:0012:20, 3:304:20, and by appointment 

Current Courses: 
Fall, 2001 & Spring, 2002


Personal Background: 


Degrees: 
University
of California at Santa Barbara, 1976  Ph.D. in mathematics 

Teaching Experience: 


Membership in professional societies: 


Professional Service: 


Grants and Awards 


Talks 
* 1. AMS Special session on combinatorial matrix theory. Hayward, CA; April 1977. 2. NSF conference on linear and multilinear algebra. Santa Barbara, CA; December 1977. 3. AMS special session on nonassociative algebras and applications. Honolulu, HI; March 1979. 4. NSF conference on linear algebra and matrix theory. Auburn, AL; March 1980. * 5. Polish Academy of Sciences international conference on Schur Functors in algebra and geometry. Torun, Poland; August 1980. * 6. Second Irish Mathematical Society Matrix Theory Conference. University College, Dublin; October 1980. * 7. Colloquium lecture, University of Wales, Aberystwyth, Wales; May 1981. * 8. Colloquium lecture, Institute fur Geometrie and Praktische Mathematik. Aachen, Germany; June 1981. 9. First Utah State University Matrix Theory Conference. Logan, UT; June 1983. *10.
Colloquium lecture, University of Waterloo.
Waterloo, Canada; July 1983.
11. AMS meeting.
San Luis Obispo, CA; November 1983. *12.
Third Irish Mathematical Society Matrix Theory Conference.
University College, Dublin; March 1984.
13. SIAM
Conference on Applied Matrix Theory.
Raleigh, NC; April 1985.
14. Conference on
Combinatorial Matrix Theory. Hayward,
CA; July 1985.
15. Seventeenth
Southeastern Conference on Graph Theory, Combinatorics, and Computing.
Boca Raton, FL; February 1986.
16. Second
Utah State University Matrix Theory Conference. Logan, UT; January 1987.
17. Combinatorial
Matrix Analysis Conference. University
of Victoria, British Columbia; May 1987. *18.
Colloquium lecture, Western Washington University.
Bellingham, WA; May 1987.
19. Second
Southern California Matrix Conference, UCSB.
Santa Barbara, CA; November 1987.
20. AMS special
session on modern trends in matrix analysis. Atlanta, GA; January 1988. *21
Fourth Irish Mathematical Society Matrix Theory Conference. University College, Dublin; March 1988
22. Third Southern
California Matrix Conference, UCSB. Santa
Barbara, CA; November 1988.
23. International
Linear Algebra Society Meeting, BYU.
Provo, UT; August 1989.
24. Directions
in Matrix Theory, Auburn, Alabama; March 1990. *25.
International Linear Algebra Society Meeting, University of West
Florida; Pensacola; March 1993. *26.
Workshop on Nonnegative Matrices.
Haifa, Israel; May 1993. *27.
Conference on Numerical Ranges.
University of Coimbra; Portugal; August 1994. *28.
International Linear Algebra Society Meeting, Erasmus University;
Rotterdam, The Netherlands; August 1994. *29.
Colloquium lecture, Auburn University.
Auburn, AL; October 1994. *30.
Tenth Southern California Matrix Theory Conference. CSUN,
Northridge CA; November 1996. * Invited talk. 

Other Conferences attended 
1. NSF
Conference on theoretical matrix theory, UCSB. Santa Barbara, CA; December 1973. 2. AMS Winter Meeting. Biloxi, MS; January 1979.
3. AMS
Regional Meeting. Birmingham, AL;
April 1983.
4. AMS
Summer Meeting and matrix miniconference. Toronto,
Ontario, Canada; August 1982.
5. Johns
Hopkins Lecture Series on Combinatorial Matrix Analysis. Baltimore, MD; June
1985.
6. International
Congress of Mathematicians. Berkeley,
CA; August 1986.
7. First
Southern California Matrix Conference, SDSU.
San Diego, CA; November 1986.
8. Johns
Hopkins Lecture Series on Matrix Spectral Inequalities.
Baltimore, MD; June 1988.
9. AMS
Winter Meeting and short course. Phoenix,
AZ; January 1989. 10.
Fourth Southern California Matrix Conference, UCSD.
La Jolla, CA; November 1989. 11.
SPIE International Symposium on Optical and Optoelectronic Applied
Science and Engineering. San Diego, CA; July, 1990. 12.
Fifth Southern California Matrix Conference, UCSB.
Santa Barbara, CA; November 1990. 13. SIAM Conference on Linear Algebra, Signals, Systems and Control. San Francisco, CA; November 1990. 14. NSFCBMS Regional Research Conference on Qualitative and Structured Matrix Theory. Georgia State University, Atlanta, GA; August 1991. 15.
IMA Tutorial on Matrix Computations.
University of Minnesota; Minneapolis, MN; September 1991. 16. SIAM Conference on Applied Linear Algebra. University of Minnesota, Minneapolis MN; September 1991. 17. IMA Workshop on Sparse Matrix Computations. University of Minnesota, Minneapolis MN; October 1991. 18. AMS Regional Meeting and Special Session on Graph Theory. North Dakota State University, Fargo ND; October 1991. 19. IMA Workshop on GraphTheoretic Problems in Linear Algebra. University of Minnesota, Minneapolis MN; November 1991. 20. NSF/ATLAST Workshop on MATLAB in Linear Algebra, West Valley College, Saratoga CA; June 1992. 21. NSF Undergraduate Faculty Enhancement Workshop on Algorithmic Number Theory. California State University, Fresno CA; June 1992. 22. Eighth Haifa Matrix Theory Conference. Technion, Haifa, Israel; June 1993. 23. NSF/CBMS Workshop on Recent Advances in Algebraic Graph Theory. California State University, Fresno CA; June 1994. 24. PROMPT Workshop Mathematics Courses for Preservice Elementary Teachers. Humboldt State University, Arcata CA; July 1994. 25. CMC Meeting on K12 Education, Palm Springs, CA; November 1994. 26. AMS Annual Meeting. San Francisco, CA; January 1995. 27. NSF/CBMS Workshop on Parallel Matrix Computations. University of San Francisco, San Francisco, CA; June 1995. 28. Canadian Mathematical Society Summer Meeting. University of Calgary, Calgary, Alberta, Canada; June 1996. 29. Western Canadian Linear Algebra Meeting. Kananaskis Village, Alberta, Canada; June 1996. 30. Crypography Conference. University of Arizona, Tucson AZ; March 1997. 31. Eighth Auburn Combinatorics Conference. Auburn University, Auburn, AL; March 1997. 

Publications 
1.
A note on the dimension of an orbital subspace.
Linear Algebra and its Applications, 17(1977) 283286; MR58:22131. 2.
Isometries of matrix algebras.
(with Marvin Marcus). Journal of Algebra, 47(1977) 180189;
MR56:3039. 3.
Decomposable tensors as a quadratic variety.
Proceedings of the American Mathematical Society, 64(1977) 227230;
MR57:12542. 4. Offdiagonal elements of normal matrices. Journal of Research of the National Bureau of Standards, 81B(1977) 4144; MR56:15679. 6.
Certain isometries of rectangular complex matrices. Linear Algebra and its Applications, 29(1980) 161171;
MR81d:15007. *7.
Scheduling Spacelab experiments (with Frank Mathis).
NASA Contractors Report 161511 (1980). **8.
Character derived matrix inequalities.
Proceedings, Conference on Schur Functors, Torun, 1980. 9. Characterizations of sign patterns of inversepositive matrices (with Miroslav Fiedler).Linear Algebra and its Applications, 40(1981) 237245. MR82i:15030. 10. Spectral radius and seminorms in finite dimensional algebras II (with Peter Johnson). Colloquium Mathematicum, 46(1982) 8588; MR84j:46079. 11. Permutation matrix groups with prescribed sum (with Dean Hoffman and J.R. Wall). Linear Algebra and its Applications, 45(1982) 2934; MR83f:15007. *12. A scheduling algorithm for Spacelab telescope observations. NASA Contractors Report 162051 (1982). 13. Positive definite completions of partial Hermitian matrices (with C.R. Johnson, E. Sa, and H. Wolkowicz). Linear Algebra and its Applications 58(1984) 109124; MR85d:05169. 14.
Improving Hadamard's inequality (with C.R. Johnson, E. Sa,
and H. Wolkowicz). Linear and
Multilinear Algebra 14(1984) 305322; MR87b:15024. 15.
An algorithm for the second immanant with R. Merris). Mathematics
of Computation 43:168(1984) 589591; MR85i:15008. *16.
A note on maximizing the permanent of a positive definite
Hermitian matrix (with C.R.Johnson, E. Sa, and H. Wolkowicz).
Emory University, Department of Mathematics Technical Report Number
15, 1985 **17.
Computation of immanants.
Linear Algebra and its Applications 68 (1985) 252254. 18. An inequality for the second immanant. Linear and Multilinear Algebra 18 (1985) 147152. MR 87e:20026. 19. A note on maximizing the permanent of a positive definite Hermitian matrix, given the eigenvalues (with C.R. Johnson, E. Sa, and H. Wolkowicz). Linear and Multilinear Algebra 19 (1986) 389394. MR 88b:15006. 20. A Hadamard dominance theorem for a class of immanants (with R. Merris and W. Watkins). Linear and Multilinear Algebra 19 (1986) 167171. MR 87g:15008. 21. Markov chains and tensor multiplications. Journal of Algebra 109 (1987) 1424. MR 88k:15034. 22. A Fischer inequality for the second immanant (with R. Merris). Linear Algebra and its Applications 87 (1987) 7783. MR 88d:15009. 23. Normal matrices (with C.R. Johnson, E. Sa, and H. Wolkowicz). Linear Algebra and its Applications 87 (1987) 213225. MR 88a:15045. 24. A Hadamard inequality for the second immanant (with R. Merris). Journal of Algebra 111 (1987) 343346.MR 88k:15008. 25. A Hadamard inequality for the third and fourth immanants (with R. Merris). Linear and Multilinear Algebra 21 (1987) 201209. MR 89k:15038. *26. Current Trends in Matrix Theory. (Conference proceedings, coedited with Frank Uhlig), pp. 1435. Elsevier North Holland, 1987. 27. Conjectures on permanents (with R. Merris). Linear and Multilinear Algebra 21 (1987) 419427. MR 89b:15006. 28. Algebraic connectivity of trees (with R. Merris). Czechoslovak Mathematica Journal 37 (1987) 660670. MR 89a:05053. 29. A bound for the complexity of a simple graph (with R. Merris). Journal of Discrete Mathematics 69 (1988) 9799. MR 89j:05066. 30. Cones in the group algebra related to Schur's determinantal inequality (with R. Merris and W. Watkins). Rocky Mountain Journal of Mathematics 18 (1988) 137146. MR 89e:15011. **31. Factorization of bipartite graphs. Linear Algebra and its Applications 104 (1988) 216219. 32. Cutpoints, lobes, and the spectra of graphs (with R. Merris). Portugaliae Mathematica 45 (1988) 18. MR 89f:05118 33. Bipartite completely positive matrices (with A. Berman). Proceedings of the Cambridge Philosophical Society 103 (1988) 269276. MR 88k:15022. 34. Permanental inequalities for correlation matrices (with S. Pierce). SIAM Journal of Matrix Analysis 9 (1988). 194201. MR 89i:15009. **35. Eigenvalues and eigenvectors of the Laplacian. Linear Algebra and its Applications 107 (1988) 332335. 36. The Laplacian spectrum of a graph (with R. Merris and V.S. Sunder). SIAM Journal of Matrix Analysis 11 (1990) 218238. 37. Ordering trees by algebraic connectivity (with R. Merris). Graphs and Combinatorics 6 (1990) 5361. 38.
Extremal bipartite matrices (with S. Pierce).
Linear Algebra and its Applications 131 (1990) 3950. 39.
Extremal correlation matrices (with S. Pierce and W.
Watkins). Linear
Algebra and its Applications 134 (1990) 6370. 40.
Coalescence, majorization, edge valuations, and the Laplacian
spectra of graphs (with R. Merris).
Linear and Multilinear Algebra
27 (1990) 139146. 41.
Large eigenvalues of the Laplacian (with G. Zimmermann).
Linear and Multilinear Algebra 28 (1990) 4547.
42. Extremal
positivesemidefinite doubly stochastic matrices (with S. Pierce).
Linear Algebra and its Applications 150 (1991) 107117. 43. On the geometry and Laplacian of a graph. Linear Algebra and its Applications 150 (1991) 167178. **44. Extreme doubly nonnegative matrices with prescribed row sums Linear Algebra and its Applications 162(1992) 754757. 45. Nonchordal positive semidefinite stochastic matrices (with R. Loewy and S. Pierce). Linear and Multilinear Algebra 32 (1992) 107113. 46. Laplacian unimodular equivalence of graphs (with R. Merris and W. Watkins)  . Combinatorial and GraphTheoretic Problems in Linear Algebra, IMA Volumes in Mathematics and it's Applications, vol. 50, SpringerVerlag 1993 (edited by R. Brualdi, S. Friedland and V. Klee) pp. 175180. 47. The Laplacian spectrum of a graph II (with R. Merris). SIAM Journal of Discrete Mathematics 7 (1994) 221229. 48. A biography of Marvin Marcus Linear Algebra and its Applications 201 (1994) 120. 49. Spectral bounds derived from quadratic forms on decomposable tensors (with J. Ross, S. Pierce and C.K. Li). Linear Algebra and its Applications 201 (1994) 181198. 50. Eigenvalues and the degree sequences of graphs. Linear and Multilinear Algebra 39 (1995) 133136. 51. Decomposably Nonnegative Matrices (with S. Pierce). Linear and Multilinear Algebra, 41 (1996) 6379. * Not in refereed journals ** Part of a conference report. 
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