Decomposition of a Hermitian matrix into a sum of a fixed number of orthoprojections

• Date: 2020
• Main Authors: Rabanovich, V. I., Рабанович, В. І.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2020
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2378
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We prove that any Hermitian matrix, whose trace is integer and all eigenvalues lie in $[1+1/(k-3),k-1-1/(k-3)],$ is a sum of $k$ orthoprojections. For sums of $k$ orthoprojections, it is shown that the ratio of the number of eigenvalues not exceeding 1 to the number of eigenvalues not less than 1, t...