Characterization of supercommuting matrices

For a given n–by–n matrix A, we consider the set of matrices which commute with A and all of whose principal submatrices commute with the corresponding principal submatrices of A. The properties of this set are examined, with particular attention to its dimension.

[1]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[2]  W. E. Roth,et al.  On $k$-commutative matrices , 1936 .