The enhanced principal rank characteristic sequence for skew-symmetric matrices

Abstract The enhanced principal rank characteristic sequence (epr-sequence) was originally defined for an n × n real symmetric matrix or an n × n Hermitian matrix. Such a sequence is defined to be l 1 l 2 ⋯ l n where l k is A , S , or N depending on whether all, some, or none of the matrix principal minors of order k are nonzero. Here we give a complete characterization of the attainable epr-sequences for real skew-symmetric matrices. With the constraint that l k = 0 if k is odd, we show that nearly all epr-sequences are attainable by skew-symmetric matrices, which is in contrast to the case of real symmetric or Hermitian matrices for which many epr-sequences are forbidden.