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On a Combinatorial Result of R. A. Brualdi and M. Newman

Published online by Cambridge University Press:  20 November 2018

Marvin Marcus  and
Stephen Pierce
Marvin Marcus
Affiliation:
University of California, Santa Barbara, California
Stephen Pierce
Affiliation:
University of California, Santa Barbara, California
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Let H be a subgroup of Sn and let A be an n-square matrix over a field ƒ. Following Schur (7) we define the generalized matrix function dH(A) by

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1056 - 1067
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

1.

The research of this author was supported by the Air Force Office of Scientific Research under grants AFOSR 698-65 and 698-67.

References

1. Brualdi, R. A. and Newman, M., Inequalities for the permanental minors of non-negative matrices, Can. J. Math. 18 (1966), 608–615.Google Scholar
2. Marcus, M. and Mine, H., Generalized matrix functions, Trans. Amer. Math. Soc. 116 (1965), 316–329.Google Scholar
3. Marcus, M. and Mine, H., A survey of matrix theory and matrix inequalities (Allyn and Bacon, Boston, 1964).Google Scholar
4. Marcus, M. and G. W. Soûles, Inequalities for combinatorial matrix functions, J. Combinatorial Theory 2 (1967), 145–163.Google Scholar
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7. Schur, I., Ûber endliche Gruppen und Hermitesche Formen, Math. Z. 1 (1918), 184–207.Google Scholar
8. Wedderburn, J. H. M., Lectures on matrices (Amer. Math. Soc. Colloq. Publ., Vol. 17, Providence, R.I., 1934).10.1090/coll/017CrossRefGoogle Scholar