Minimal realizations of supersymmetry for matrix Hamiltonians

• Weak and strong minimization of a matrix intertwining operator.
• Criterion of strong minimizability from the right of a matrix intertwining operator.
• Conditions of existence of a constant symmetry matrix for a matrix Hamiltonian.
• Method of constructing of a matrix Hamiltonian with a given constant symmetry matrix.
• Examples of constructing of 2×22×2 matrix Hamiltonians with a given symmetry matrix.

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 2×22×2 matrix Hamiltonians with given symmetry matrices for the cases of different structure of Jordan form of these matrices are elucidated.