Extension of a Formula by Cayley to Symmetric Determinants
- 1 October 1948
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Edinburgh Mathematical Society
- Vol. 8 (2) , 73-75
- https://doi.org/10.1017/s0013091500024810
Abstract
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 formulawhere 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 .Keywords
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