The principal rank characteristic sequence over various fields

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Date
2014Author
Barrett, Wayne
Butler, Steve
Catral, Minnie
Fallat, Shaun
Hall, Tracy
Hogben, Leslie
van den Driessche, Pauline
Young, Michael
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Given an n-by-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.