To solving multiparameter problems of algebra. 6. Spectral characteristics of polynomial matrices

For a $q$-parameter polynomial $m\times n$ matrix $F$ of rank $\rho$, solutions of the equation $Fx=0$ at points of the spectrum of the matrix $F$ determined by the $(q-1)$-dimensional solutions of the system $Z[F]=0$ are considered. Here, $Z[F]$ is the polynomial vector whose components are all possible minors of order $\rho$ of the matrix $F$. A classification of spectral pairs in terms of the matrix $A[F]$, with which the vector $Z[F]$ is associated, is suggested. For matrices $F$ of full rank, a classification and properties of spectral pairs in terms of the so-called levels of heredity of points of the spectrum of $F$ are also presented.