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A note on an identity of Jacobi's

Published online by Cambridge University Press:  31 October 2008

Nancy Walls
Nancy Walls
Affiliation:
University College, Southampton
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That the determinant

where hr is the rth complete homogeneous symmetric function in a set of n arguments, is equal to the quotient of a particular pair of alternants was shown essentially by Jacobi in 1841 and by Trudi in 1864. The present note exhinits this well-know relation, (3), as the immediate consequence of a simple matrix equality.

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 37 , January 1949 , pp. 7 - 9
Copyright
Copyright © Edinburgh Mathematical Society 1949