TY - JOUR
AU - V. I. Rabanovich
PY - 2020/04/29
Y2 - 2020/11/01
TI - Decomposition of a Hermitian matrix into a sum of a fixed number of orthoprojections
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 72
IS - 5
SE - Research articles
DO - 10.37863/umzh.v72i5.2378
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/2378
AB - 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, taking into account the multiplicity, is not greater than $k-1$. Examples of Hermitian matrices that satisfy the ratio for eigenvalues and, at the same time, can not be decomposed into a sum of $k$ orthoprojections are also suggested.
ER -