proof of generalized Ruiz’s identity
Consider the polynomials . Then, for every positive natural number ,
Consider the matrices defined by and .
Therefore, by Ruiz’s identity, for every and for every such that . This means that is an upper triangular matrix whose main diagonal is . Since the determinant of such a matrix is the product of the elements in the main diagonal, we get that . It is easy to see that itself is lower triangular with determinant . Therefore . ∎
|Title||proof of generalized Ruiz’s identity|
|Date of creation||2013-03-22 14:32:02|
|Last modified on||2013-03-22 14:32:02|
|Last modified by||GeraW (6138)|