The enhanced principal rank characteristic sequence over a field of characteristic 2
نویسندگان
چکیده
The enhanced principal rank characteristic sequence (epr-sequence) of an n× n symmetric matrix over a field F was recently defined as `1`2 · · · `n, where `k is either A, S, or N based on whether all, some (but not all), or none of the order-k principal minors of the matrix are nonzero. Here, a complete characterization of the epr-sequences that are attainable by symmetric matrices over the field Z2, the integers modulo 2, is established. Contrary to the attainable epr-sequences over a field of characteristic 0, this characterization reveals that the attainable epr-sequences over Z2 possess very special structures. For more general fields of characteristic 2, some restrictions on attainable epr-sequences are obtained.
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