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Extension of a Formula by Cayley to Symmetric Determinants
Published online by Cambridge University Press: 20 January 2009
Extract
It has been proved by CAYLEY that if x11, x12, x21 … are independent variables, x = det (xik), ξ = det (ξik), (i, k = 1, … n) where ξik =∂/∂xik then by formal derivation ξxα = α(α + 1)…(α + n − 1)xα−1. This is a special case of the formula
where m=1,…,n and with i = i1,..im; k= k1,…km and xi,… is the algebracial complement of i = i1,..im; k = k1,…km, in .
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- Copyright © Edinburgh Mathematical Society 1948
References
page 73 note 1 Turnbull, H. W., “The Theory of Determinants, Matrices, and Invariants,” London, (1928), p. 116.Google Scholar
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