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[Jon Zingale]

Tom,

Perhaps one of the most common usages of the Kronecker delta,
and a usage we skirted in the discussion, is to establish biorthogonality
between a vector space and its dual space. The Kronecker delta arises
when given an indexed basis and its indexed dual set (which may or
may not span the dual space), we take inner products of vectors in
the first with vectors in the second. Because of linear independence
in both sets, the inner product will take the value 1 when the vectors
correspond and 0 otherwise. The Kronecker delta, in this case, is a
manifestation of inner products and duality.

Jon



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