Journal or Book Title
Linear Algebra and its Applications
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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Barrett, Wayne; Butler, Steve; Catral, Minerva; Fallat, Shaun M.; Hall, H. Tracy; Hogben, Leslie; van den Driessche, P.; and Young, Michael, "The principal rank characteristic sequence over various fields" (2014). Mathematics Publications. 197.