Linear transformations of variance/covariance matrices

P.J.A. Parois, M. Lutz

    Research output: Contribution to journalArticleAcademicpeer-review

    Abstract

    Many applications in crystallography require the use of linear transformations on parameters and their standard uncertainties. While the transformation of the parameters is textbook knowledge, the transformation of the standard uncertainties is more complicated and needs the full variance/covariance matrix. For the transformation of second-rank tensors it is suggested that the 3 3 matrix is re-written into a 9 1 vector. The transformation of the corresponding variance/covariance matrix is then straightforward and easily implemented into computer software. This method is applied in the transformation of anisotropic displacement parameters, the calculation of equivalent isotropic displacement parameters, the comparison of refinements in different space-group settings and the calculation of standard uncertainties of eigenvalues.
    Original languageEnglish
    Pages (from-to)383-390
    Number of pages8
    JournalActa crystallographica. Section A, foundations of crystallography
    VolumeA67
    DOIs
    Publication statusPublished - 2011

    Fingerprint

    Dive into the research topics of 'Linear transformations of variance/covariance matrices'. Together they form a unique fingerprint.

    Cite this