### 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 language | English (US) |
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Pages (from-to) | B558-B562 |

Journal | Physical Review |

Volume | 136 |

Issue number | 2B |

DOIs | |

State | Published - 1964 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

Zwanziger, D. (1964). Simple theorem on Hermitian matrices and an application to the polarization of vector particles.

*Physical Review*,*136*(2B), B558-B562. https://doi.org/10.1103/PhysRev.136.B558