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Extension of a Formula by Cayley to Symmetric Determinants

Published online by Cambridge University Press:  20 January 2009

Lars Gårding
Lars Gårding
Affiliation:
The Institute of Mathematics, Lund University, Lund, Sweden.
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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 .

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 8 , Issue 2 , October 1948 , pp. 73 - 75
Copyright
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