Research InterestsMy doctoral dissertation research was on the fundamental matrix of constrained minimization and dealt with generalized inverses of matrices. After that I did further work on generalized inverses, and also research on integer matrices and con-similarity of matrices. My recent research is in the area of combinatorial matrix theory, with an emphasis on sign pattern and ray pattern matrices. Recent research also includes graph theory, eigenvalue interlacing, and tournament matrices. I am a member of the American Mathematical Society and the International Linear Algebra Society .
M. Arav, F. J. Hall, K. Kaphle, Z. Li, and N. Manzagol, Spectrally arbitrary tree sign patterns of order 4, submitted to the Electronic Linear Algebra Journal.
A. Berman, M. Catral, L. M. Dealba, A. Elhashash, F. J. Hall, L. Hogben, I. J. Kim, D. D. Olesky, P. Tarazaga, M. J. Tsatsomeros, and P. v. d. Driesssche, Sign patterns that allow eventual positivity, submitted to the Electronic Linear Algebra Journal.
M. Arav, F. J. Hall, Z. Li, and B. Rao, ZPC matrices and zero cycles, International Journal of Combinatorics (2009), Article ID 520923, 5 pages.
M. Arav, F. J. Hall, Z. Li, and B. Rao, Rational solutions of certain matrix equations, Lin. Alg. and Appl. 430(2009), 660-663.
M. Arav, F. J. Hall, Z. Li, A. Merid, and Y. Gao, Sign pattern matrices that require almost unique rank, Lin. Alg. and Appl. 430(2009), 7-16.
F. J. Hall, K. Patel and M. Stewart, Interlacing results on matrices associated with graphs, The Journal of Combinatorial Mathematics and Combinatorial Computing 68(2009), 113-127.
M. Arav, F. J. Hall, and Z. Li, A Cauchy-Schwarz inequality for triples of vectors, Mathematical Inequalities and Applications 11(2008), 629-634.
M. Arav, J. H. Bevis, and F. J. Hall, Inherited LU-factorizations, Lin. Alg. and Appl. 427(2007), 26-41.
F. J. Hall and Z. Li, Sign pattern matrices, in the Handbook of Linear Algebra, published by Chapman & Hall/CRC, Chapter 33 (invited), 2007.
M. Arav, F. J. Hall, S. Koyuncu, Z. Li, and B. Rao, Rational realizations of the minimum rank of a sign pattern matrix, Lin. Alg. and Appl. 409(2005), 111-125.
F. J. Hall, Z. Li and J. Stuart, Reducible powerful ray pattern matrices, Lin. Alg. and Appl. 399(2005), 125-140.
G. Chen, G. Davis, F. J. Hall, K. Patel, and M. Stewart, An interlacing result for Normalized Laplacians, SIAM J. on Discrete Mathematics 18(2004), 353-361.
F. J. Hall, Z. Li and B. Rao, From Boolean to sign pattern matrices, Lin. Alg. and Appl. 393(2004), 233-251.
F. J. Hall and Z. Li, Sign patterns, inverses, and generalized inverses – a brief survey, Numerical Math. J. of Chinese Universities 12(Supplement)(2003), 8-11.
G. Chen, F. J. Hall, Z. Li, and B. Wei, On ranks of matrices associated with trees, Graphs and Combinatorics 19(2003), 323-334.
F. J. Hall, Z. Li and J. Stuart, Irreducible powerful ray pattern matrices, Lin. Alg. and Appl. 342(2002), 47-58.
F. J. Hall and Z. Li, Inertia sets of symmetric sign pattern matrices, Numerical Math. J. of Chinese Universities 10(2001), 226-240.
F. J. Hall, Z. Li and D. Wang , Symmetric sign pattern matrices that require unique inertia, Lin. Alg. and Appl. 338(2001), 153-169.
G. Chen, F. J. Hall, A. E. Kezdy, Z. Li, and H. Zhou, Isomorphisms involving reversing arcs of digraphs, The Journal of Combinatorial Mathematics and Combinatorial Comp 36(2001), 155-160.
C. Eschenbach, F. Hall, R. Hemasinha, S. J. Kirkland, Z. Li, B. L. Shader, J. L. Stuart, and J. R. Weaver, Properties of tournaments among well matched players, The American Mathematical Monthly 107(2000), 881-892.
C. Eschenbach, F. Hall, R. Hemasinha, S. J. Kirkland, Z. Li, B. L. Shader, J. L. Stuart, and J. R. Weaver, On almost regular tournament matrices, Lin. Alg. and Appl. 306(2000), 103-121.
C. A. Eschenbach, F. J. Hall, and Z. Li, Eigenvalue distribution of certain ray patterns, Czechoslovak Mathematical Journal 50(125) (2000), 749-762.
A Few of My Mathematical Ancestors
Carl D. Meyer (dissertation advisor)
Other ancestors include David Hilbert, Joseph Lagrange, and Carl Gauss.
I was born and grew up in San Antonio, Texas. On my mother's side, my grandfather at a young age came from a small village in Moravia (which is now part of the Czech Republic) to Cameron in central Texas. These grandparents had fifteen children (some died young) plus an adopted child, and the family worked hard in farming cattle, cotton, and other crops. As a result of the conditions, my mother was able to receive only a sixth grade education. My father originally came from Louisiana to Texas. His parents died when he was young and he was raised by an aunt. He always had to work while he was in school, but he did have one year in college. I have two sisters and a brother. Formerly, I served in Nigeria as a member of the United States Peace Corps. Prior to coming to Georgia State University, I was a faculty member at Pembroke State Universty. Pembroke, NC is the center of the Lumbee Indian community. I have been at Georgia State University since 1978. My wife, Anne, and I have two children, Genevieve and Timothy. I enjoy tennis, hiking, traveling, and volunteer work.