  The notions of weak and strong minimizability of a matrix intertwining
operator are introduced. Criterion of strong minimizability of a matrix
intertwining operator is revealed. Criterion and sufficient condition of
existence of a constant symmetry matrix for a matrix Hamiltonian are presented.
A method of constructing of a matrix Hamiltonian with a given constant symmetry
matrix in terms of a set of arbitrary scalar functions and eigen- and
associated vectors of this matrix is offered. Examples of constructing of
$2\times2$ matrix Hamiltonians with given symmetry matrices for the cases of
different structure of Jordan form of these matrices are elucidated.
