Using q-calculus to study LDLt factorization of a certain Vandermonde matrix
نویسندگان
چکیده
منابع مشابه
Vandermonde Factorization of a Hankel Matrix ?
We show that an arbitrary Hankel matrix of a nite rank admits a Vandermonde decomposition: H = V T DV , where V is a con-uent Vandermonde matrix and D is a block diagonal matrix. This result was rst derived by Vandevoorde; our contribution here is a presentation that uses only linear algebra, speciically, the Jordan canonical form. We discuss the choices for computing this decomposition in only...
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It is shown that an innnite Hankel matrix of a nite rank (or a nite Hankel matrix) admits a generalized Vandermonde decomposition H = V T DV , where V is a generalized Vandermonde matrix, and D is a block diagonal matrix. The full structure of this decomposition was rst fully discussed by Vandevoorde 9], but the development here is based solely on linear algebra considerations, speciically the ...
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We consider a special class of the generalized Vandermonde matrices and obtain an LU factorization for its member by giving closed-form formulae of the entries of L and U . Moreover, we express the matrices L and U as products of 1-banded (bidiagonal) matrices. Our result is applied to give the closed-form formula of the inverse of the considered matrix.
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ژورنال
عنوان ژورنال: Operators and Matrices
سال: 2018
ISSN: 1846-3886
DOI: 10.7153/oam-2018-12-45