Vandermond determinant

In Ref. [76], an elegant proof was instigated through the theory of Vandermonde determinants. Here, we will offer an alternative route, i.e., by directly computing (n > 1)... 

This determinant is nonsingular. This is due to the inequality Vk =/=0 that holds true because the roots Uj are never equal to m, for/ / j. The quotient Vjt+i/Vjfc is computed via the Vandermonde determinant with the following ... 

To get the correct results the eigenvalues with the index k have to be omitted. As discussed in eq. (2.54), IVJ is the Vandermond determinant given by... 

Taking all brackets, of which the eigenvalues are part, equal to one, the different values of are obtained from the Vandermond determinant V. ... 

If equal eigenvalues result in a Vandermond determinant, which equals zero, eq. (2.53) can no longer be solved with respect to p,. With... 

In this equation, the matrix V represents the so-called Vandermond s matrix [17] with the determinant... 

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