A matrix interpretation of identities of the classical calculus is given by using the Zavadskij’s -transformation and its properties. Such transformation allows to describe in a simple fashion solutions of the homogeneous biquadratic problem which in some cases can be reduced to the semilinear Kronecker problem.

indecomposable representation, homogeneous biquadratic problem, Kronecker matrix problem, matrix problem, poset representation, semilinear Kronecker problem, -transformation.