# Some Results on Vandermonde Matrices with an Application to Time Series Analysis

@article{Klein2003SomeRO, title={Some Results on Vandermonde Matrices with an Application to Time Series Analysis}, author={Andr{\'e} Klein and Peter Spreij}, journal={SIAM J. Matrix Anal. Appl.}, year={2003}, volume={25}, pages={213-223} }

In this paper we study Stein equations in which the coefficient matrices are in companion form. Solutions to such equations are relatively easy to compute as soon as one knows how to invert a Vandermonde matrix (in the generic case where all eigenvalues have multiplicity one) or a confluent Vandermonde matrix (in the general case). As an application we present a way to compute the Fisher information matrix of an autoregressive moving average (ARMA) process. The computation is based on the fact…

## 9 Citations

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We provide explicit representations of the null space $\mathcal{S}$ of adjoints of companion-related matrices and of certain rectangular generalized Vandermonde matrices of block Toeplitz type which…

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An approach is presented to get interconnections between the Fisher information matrix of an ARMAX process and a corresponding solution of a Stein equation. The case of algebraic multiplicity greater…

### UvA-DARE ( Digital Academic Repository ) Recursive solution of certain structured linear systems

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We provide explicit representations of the null space S of adjoints of companionrelated matrices and of certain rectangular generalized Vandermonde matrices of block Toeplitz type which are…

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### Block Vandermonde Matrices of Matrix Polynomial’s Solvents

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Some properties of these matrices, and iterative algorithms to compute the determinant and the inverse of a block Vandermonde matrix are given, and a parallelization of these algorithms is presented.

### Extreme Points of the Vandermonde Determinant on the Sphere and Some Limits Involving the Generalized Vandermonde Determinant

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- 2020

The values of the determinant of Vandermonde matrices with real elements are analyzed both visually and analytically over the unit sphere in various dimensions. For three dimensions some generalized…

### Positivities of Vandermonde tensors

- Mathematics, Computer Science
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The positivities of Vandermonde tensors are investigated, including their positive definiteness and total positivity, and it is shown that a VandermondE tensor generated by a positive increasing ordered vector is totally positive.

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