The principal rank characteristic sequence over various fields

Date
2014-10-15
Authors
Barrett, Wayne
Butler, Steve
Catral, Minerva
Hogben, Leslie
Fallat, Shaun
Hall, H. Tracy
Hogben, Leslie
van den Driessche, P.
Young, Michael
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Abstract

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.

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<p>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." <em>Linear Algebra and its Applications</em> 459 (2014): 222-236. DOI: <a href="http://dx.doi.org/10.1016/j.laa.2014.06.045" target="_blank">10.1016/j.laa.2014.06.045</a>. Posted with permission.</p>
Keywords
Principal rank characteristic sequence, Minor, Rank, Symmetric matrix, Hermitian matrix, Finite field
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