Generalized Vandermonde determinants
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چکیده
منابع مشابه
Generalized Vandermonde Determinants over the Chebyshev Basis
It is a well known fact that the generalized Vandermonde determinant can be expressed as the product of the standard Vandermonde determinant and a polynomial with nonnegative integer coefficients. In this paper we generalize this result to Vandermonde determinants over the Chebyshev basis. We apply this result to prove that the number of real roots in [1;1] of a real polynomial is bounded by th...
متن کاملTropicalization and Irreducibility of Generalized Vandermonde Determinants
We find geometric and arithmetic conditions in order to characterize the irreducibility of the determinant of the generic Vandermonde matrix over the algebraic closure of any field k. We also characterize those determinants whose tropicalization with respect to the variables of a row is irreducible.
متن کاملOn the Irreducibility of Generalized Vandermonde Determinants
We find geometric and arithmetic conditions on a finite set of integer exponents and the characteristic of a field k in order to characterize the irreducibility of the determinant of the generic Vandermonde matrix determined by these exponents in the algebraic closure of k. Tools from Tropical Geometry are then applied in order to characterize those determinants that are irreducible over any fi...
متن کاملA Generalized Vandermonde Determinant
Interpolation theory suggests a generalization of the usual Vandermonde determinant to numbers with multiplicities. We prove a discriminant formula for this generalized Vandermonde determinant and give an application to the Hermite interpolation problem.
متن کاملThe Generalized Vandermonde Matrix
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1929
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1929-1501494-2