 Correlation between two projected matrices under isometry constraintsCatherine Fraikin, Yurii Nesterov and Paul van Dooren No 2005080, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) Abstract: In this paper, we consider the problem of correlation between the projections of two square matrices. These matrices of dimensions m x[mult.] m and n x[mult.] n are projected on a subspace of lower-dimension k under isometry constraints. We maximize the correlation between these projections expressed as a trace function of the product of the projected matrices. First we connect this problem to notions such as the generalized numerical range, the field of values and the similarity matrix. We show that these concepts are particular cases of our problem for choices of m, n and k. The formulation used here applies to both real and complex matrices. We characterize the objective function, its fixed points, its optimal value for Hermitian and normal matrices and finally upper and lower bounds for the general case. An iterative algorithm based on the singular value decomposition is proposed to solve the optimization problem. Keywords: correlation; trace maximization; generalized numerical range; isometry (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:cor:louvco:2005080 Access Statistics for this paper More papers in LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) Voie du Roman Pays 34, 1348 Louvain-la-Neuve (Belgium). Contact information at EDIRC. |
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