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A note on an identity of Jacobi's
Published online by Cambridge University Press: 31 October 2008
Extract
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.
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- Copyright © Edinburgh Mathematical Society 1949