Geodesic
Mean Value and Limit Theorems for Generalized Matrix Functions
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 982-991

Voir la notice de l'article provenant de la source Cambridge University Press

Let A = [aij] denote an n-square matrix with entries in the field of complex numbers. Denote by H a subgroup of Sn, the symmetric group on the integers 1, ..., n, and by a character of degree 1 on H. Then is the generalized matrix function of A associated with H and x; e.g., if H = Sn and χ = 1, then the permanent function. If the sequences ω = (ω1, ..., ωm) and Υ = (Υ1, ..., Υm) are m-selections, m ≦ w, of integers 1, ..., n, then A [ω| Υ] denotes the m-square generalized submatrix [aωiΥj], i, j = 1, ..., m, of the n-square matrix A. If ω is an increasing m-combination, then A [ω|ω] is an m-square principal submatrix of A. 
Nikolai, Paul J. Mean Value and Limit Theorems for Generalized Matrix Functions. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 982-991. doi: 10.4153/CJM-1969-108-6
@article{10_4153_CJM_1969_108_6,
     author = {Nikolai, Paul J.},
     title = {Mean {Value} and {Limit} {Theorems} for {Generalized} {Matrix} {Functions}},
     journal = {Canadian journal of mathematics},
     pages = {982--991},
     year = {1969},
     volume = {21},
     number = {1},
     doi = {10.4153/CJM-1969-108-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-108-6/}
}
TY  - JOUR
AU  - Nikolai, Paul J.
TI  - Mean Value and Limit Theorems for Generalized Matrix Functions
JO  - Canadian journal of mathematics
PY  - 1969
SP  - 982
EP  - 991
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-108-6/
DO  - 10.4153/CJM-1969-108-6
ID  - 10_4153_CJM_1969_108_6
ER  - 
%0 Journal Article
%A Nikolai, Paul J.
%T Mean Value and Limit Theorems for Generalized Matrix Functions
%J Canadian journal of mathematics
%D 1969
%P 982-991
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-108-6/
%R 10.4153/CJM-1969-108-6
%F 10_4153_CJM_1969_108_6

[1] 1. Beckenbach, Edwin F. and Bellman, Richard, Inequalities, Chapter I (Springer, Berlin, 1961). Google Scholar

[2] 2. Brualdi, Richard A., On the permanent and maximal characteristic root of a non-negative matrix, Proc. Amer. Math. Soc. 17 (1986), 1413–1416. Google Scholar

[3] 3. Cargo, G. T. and Shisha, O., Bounds on ratios of means, J. Res. Nat. Bur. Standards 66B (1962), 169–170. Google Scholar

[4] 4. Greub, W. H., Multilinear algebra (Springer, New York, 1967). Google Scholar

[5] 5. Hardy, G. H., Littlewood, J. E., and G. Pôlya, Inequalities, 2nd éd., Chapter II (Cambridge Univ. Press, London, 1952). Google Scholar

[6] 6. Marcus, Marvin, On two classical results of I. Schur, Bull. Amer. Math. Soc. 70 (1964), 685–688. Google Scholar

[7] 7. Marcus, Marvin, Matrix applications of a quadratic identity for decomposable symmetrized tensors, Bull. Amer. Math. Soc. 71 (1965), 360–364. Google Scholar

[8] 8. Marcus, Marvin, Lengths of tensors, pp. 163-176 of Inequalities, Proceedings of a Symposium, Wright-Patterson Air Force Base, Ohio, 1965, edited by O., Shisha (Academic Press, New York, 1967). Google Scholar

[9] 9. Marcus, Marvin and Khan, N. A., Some generalizations of Kantorovich's inequality, Portugal. Math. 20 (1961), 33–38. Google Scholar

[10] 10. Marcus, Marvin and McGregor, J. L., Extremal properties of hermitian matrices, Can. J. Math. 8 (1956), 524–531. Google Scholar

[11] 11. Marcus, Marvin and Mine, Henryk, A survey of matrix theory and matrix inequalities (Allyn and Bacon, Boston, 1964). Google Scholar

[12] 12. Marcus, Marvin and Mine, Henryk, Generalized matrix functions, Trans. Amer. Math. Soc. 116 (1965), 316–329. Google Scholar

[13] 13. Marcus, Marvin and Newman, Morris, Inequalities for the permanent function, Ann. of Math. (2) 75 (1962), 47–62. Google Scholar

[14] 14. Schur, I., Über endliche Gruppen und Hermitesche Formen, Math. Z. 1 (1918), 184–207. Google Scholar

[15] 15. Shisha, O. and Mond, B., Bounds on differences of means, pp. 293-308 of Inequalities, Proceedings of a Symposium, Wright-Patterson Air Force Base, Ohio, 1965, edited by Shisha, O. (Academic Press, New York, 1967). Google Scholar

[16] 16. Shniad, Harold, On the convexity of mean value functions, Bull. Amer. Math. Soc. 54 (1948), 770–776. Google Scholar

Cité par Sources :