The author considers the matrix equation
and its Hermitian positive definite solutions; here
complex matrix and
is the identity matrix of order
. He shows that if
is normal (i.e.
), then such a solution exists if and only if
is the spectral radius of
. The author discusses in detail the basic fixed point iterations for the equation in the case when
is nonnormal and
stands for the spectral norm for square matrices (i.e. one has
). Some of the results of I.G. Ivanov, V.I. Hasanov
and B.V. Minchev
[ibid. 326, 27-44 (2001; Zbl 0979.15007
)] are improved.