Simple theorem on Hermitian matrices and an application to the polarization of vector particles

Daniel Zwanziger

    Research output: Contribution to journalArticle

    Abstract

    It is proven that a necessary and sufficient condition for an n-dimensional Hermitian matrix to be positive definite is that it be expressible in the form =OEO, where O is a complex orthogonal matrix and E is a diagonal matrix with positive elements. This accomplishes a parametrization since O has n2-n real parameters and E has n of them. The proof is constructive, giving O and E. It is further shown that the limit forms of this expression yield all the non-negative definite matrices. The parametrization for the polarization matrix of a spin-one particle is given explicitly.

    Original languageEnglish (US)
    Pages (from-to)B558-B562
    JournalPhysical Review
    Volume136
    Issue number2B
    DOIs
    StatePublished - 1964

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

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