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The Poincaré Map in Mixed Exterior Algebra

Published online by Cambridge University Press:  20 November 2018

J. R. Vanstone
J. R. Vanstone*
Affiliation:
Department of Mathematics, University of TorontoToronto, CanadaM5S 1A1
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Abstract

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The Poincaré map of mixed exterior algebra generalizes the Hodge star operator and it plays a central rôle in the proofs of many classical identities of linear algebra. The principal purpose of this paper is to derive a new formula for it. This formula is useful in circumstances when the definition is too implicit. Several applications are discussed.

Keywords

15A75
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 2 , 01 June 1983 , pp. 129 - 136
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Greub, W. H., Multilinear Algebra (Second Edition), Springer-Verlag, New York (1978), Chapters 6 and 7.Google Scholar
2. Vanstone, J. R., Some New Identities in Mixed Exterior Algebra, C.R. Math. Rep. Acad. Sci. Canada, Vol. II (1980), no. 5.Google Scholar