Exterior products, elementary symmetric functions, and the Fischer determinant inequality

Linear Algebra and Its Applications

Volumn 255, Issue 1-3, 1997, Pages 203-242

  Pate, Thomas H ^a  

^a AUBURN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039500082     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(96)00044-4     Document Type: Article

References (27)

1. E. Fischer, Über den Hadamardschen Determinentensatz, Arch. Math. u. Phys. (3) 13:32-40 (1907).
2. J. Hadamard, Resolution d'une question relative aux déterminants, Bull. Sci. Math. 2:249-248 (1893).
3. J. Hadamard, The Psychology of Invention in the Mathematical Field, Princeton U.P., 1945, pp. 52, 128.
4. P. Heyfron, Positive Functions Defined on Hermitian Positive Semi-definite Matrices, Ph.D. Thesis, Univ. of London, England, 1989.
5. P. Heyfron, Some inequalities concerning immanants, Math. Proc. Cambridge Philos. Soc. (15) 109:15-30 (1991).
6. G. D. James and M. W. Liebeck, Permanants and immanants of Hermitian matrices, Proc. London Math. Soc. (3) 55:243-265 (1987).
7. Roger A. Horn and Charles R. Johnson, Matrix Analysis, Cambridge U.P., Cambridge, 1985.
8. E. H. Lieb, Proofs of some conjectures on permanents, J. Math. and Mech. 16:127-134 (1966).
9. Marvin Marcus, Finite Dimensional Multilinear Algebra, Vol. 2, Marcel Dekker, New York, 1973-1975.
10. R. Merris and J. A. DaSilva, Generalized Schur functions, J. Algebra 35:442-448 (1975).
11. R. Merris and W. Watkins, Inequalities and identities for generalized matrix functions, Linear Algebra Appl. 64:223-242 (1985).
12. R. Merris, The permanental dominance conjecture, in Current Trends in Matrix Theory (R. Grone and F. Uhlig, Eds.), Elsevier, New York, 1987.
13. R. Grone and R. Merris, Conjectures on permanents, Linear and Multilinear Algebra (4) 21:419-427 (1987).
14. T. H. Pate, Partitions, irreducible characters, and inequalities for generalized matrix functions, Trans. Amer. Math. Soc. (2) 325:875-894 (1991).
15. T. H. Pate, Permanental dominance and the Soules conjecture for certain right ideals in the group algebra, Linear and Multilinear Algebra (1) 24:135-149 (1989).
16. T. H. Pate, Descending chains of immanants, Linear Algebra Appl. 162-164:639-650 (1992).
17. T. H. Pate, Immanant inequalities and partition node diagrams, J. London Math. Soc. (2) 46:65-80 (1992).
18. T. H. Pate, Immanant inequalities, induced characters, and rank two partitions, J. London Math. Soc. (1) 49:40-60 (1994).
19. T. H. Pate, Tensor products, symmetric products, and permanents of positive semi-definite Hermitian matrices, Linear and Multilinear algebra (1-4) 31:27-36 (1992).
20. T. H. Pate, Psi-functions, permutations characters, and a conjecture of Merris and Watkins, Linear and Multilinear Algebra (3-4) 35:195-212 (1993).
21. T. H. Pate, Lower bounds for permanents of Gram matrices having a rank one principal submatrix, Linear Algebra Appl. 111:249-259 (1988).
22. T. H. Pate, Inequalities involving immanants, Linear Algebra Appl. 212-213:31-44 (1994).
23. T. H. Pate, Group algebras, monotonicity, and the Lieb permanent inequality, submitted for publication.
24. T. H. Pate, Inequalities relating groups of diagonal products in a Gram matrix, Linear and Multilinear Algebra 11:1-17 (1982).
25. R. M. Redheffer, A determinant inequality, in General Inequalities 1, Proceedings of the First International Conference on General Inequalities (E. F. Beckenbach, Ed.), Birkhäuser Verlag, Basel, 1978, p. 308.
26. J. Riordan, Combinatorial Identities, Wiley, New York, 1968.
27. I. Schur, Über endlicher Gruppen und Hermitische Formen, Math. Z. 1:184-207 (1918).