On the Mixed Cayley-Sylvester Resultant Matrix
For a generic n-degree polynomial system which contains n+1 polynomials in n variables, there are two classical resultant matrices, Sylvester resultant matrix and Cayley resultant matrix, lie at the two ends of a gamut of n+1 resultant matrices. This paper gives the construction of the n–1 resultant matrices which lie between the two pure resultant matrices by the combined method of Sylvester dialytic and Cayley quotient. Since the construction involves two steps, Cayley quotient and Sylvester dialytic, the block structure of these mixed resultant matrices are similar to that of Sylvester resultant matrix in large scale, and the detailed submatrices are similar to Dixon resultant matrix.
KeywordsMixed Cayley-Sylvester resultant matrix Cayley quotient Sylvester dialytic block structure
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