Matrices with few nonzero principal minors
2018
AbstractTo generalize D-nilpotent matrices that play a role in study of Druzkowski maps, we introduce quasi-D-nilpotent matrices. A matrix A is called quasi-D-nilpotent if there exists a subspace V of diagonal matrices of codimension 1 such that DA is nilpotent for all . It is proved that a quasi-D-nilpotent matrix has few nonzero principal minors. We also determine irreducible quasi-D-nilpotent matrices and the Frobenius normal forms of quasi-D-nilpotent matrices with respect to permutation similarity.
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