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On Moore-Penrose inverses of quasi-Kronecker structured matrices


Furrer, R; Heersink, D K (2012). On Moore-Penrose inverses of quasi-Kronecker structured matrices. Linear Algebra and its Applications, 436(3):561-570.

Abstract

The Moore-Penrose inverse and generalized inverse of A + X(1)X(2)*, where A. X(1), X(2) are complex matrices are given under various assumptions. We use the result to derive the Moore-Penrose inverse and inverse for bdiag(A(k)) + uv* circle times E with p complex matrices A(k), two complex p-vectors u and v and a complex matrix E. Such block structured matrices occur in hierarchical modeling of multivariate spatial or space-time Gaussian processes. For the latter we also give expressions of the determinant and of conditional variances. (C) 2011 Elsevier Inc. All rights reserved.

Abstract

The Moore-Penrose inverse and generalized inverse of A + X(1)X(2)*, where A. X(1), X(2) are complex matrices are given under various assumptions. We use the result to derive the Moore-Penrose inverse and inverse for bdiag(A(k)) + uv* circle times E with p complex matrices A(k), two complex p-vectors u and v and a complex matrix E. Such block structured matrices occur in hierarchical modeling of multivariate spatial or space-time Gaussian processes. For the latter we also give expressions of the determinant and of conditional variances. (C) 2011 Elsevier Inc. All rights reserved.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2012
Deposited On:22 Jan 2013 13:27
Last Modified:05 Apr 2016 16:18
Publisher:Elsevier
ISSN:0024-3795
Publisher DOI:https://doi.org/10.1016/j.laa.2011.07.009

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