The principal rank characteristic sequence over various fields
Hall, H. Tracy
van den Driessche, P.
Given an n x n matrix, its principal rank characteristic sequence is a sequence of length n+1 of 0s and 1s where, for k = 0, 1, . . . , n, a 1 in the kth position indicates the existence of a principal submatrix of rank k and a 0 indicates the absence of such a submatrix. The principal rank characteristic sequences for symmetric matrices over various fields are investigated, with all such attainable sequences determined for all n over any field with characteristic 2. A complete list of attainable sequences for real symmetric matrices of order 7 is reported.
This is a manuscript of an article published as Barrett, Wayne, Steve Butler, Minerva Catral, Shaun M. Fallat, H. Tracy Hall, Leslie Hogben, Pauline van den Driessche, and Michael Young. "The principal rank characteristic sequence over various fields." Linear Algebra and its Applications 459 (2014): 222-236. DOI: 10.1016/j.laa.2014.06.045. Posted with permission.