## The matrix completion problem regarding various classes of P0,1- matrices

 dc.contributor.advisor Leslie Hogben dc.contributor.author Wangsness, Amy dc.contributor.department Mathematics dc.date 2018-08-25T03:03:48.000 dc.date.accessioned 2020-06-30T08:05:57Z dc.date.available 2020-06-30T08:05:57Z dc.date.copyright Sat Jan 01 00:00:00 UTC 2005 dc.date.issued 2005-01-01 dc.description.abstract

A pattern of positions in an n x n real matrix is said to have pi-completion if every partial pi-matrix which specifies that pattern can be completed to a pi-matrix. An n x n partial matrix A (and the pattern describing the specified entries of A) is associated with a digraph G(V E) where the vertices V of G are 1, 2, 3,...,n, and an arc (i, j) [is in] E if and only if ail is specified in A. A P 0,1-matrix is a matrix in which all principal minors are non-negative and the diagonal is positive. A matrix A is sign symmetric if either aijaji > 0 or a ij = aji = 0 for all entries aij in A. A matrix A is weakly sign symmetric if aijaji > 0 for all entries aij in A. In this dissertation, all digraphs up through order 4 are classified as to whether or not every partial pi-matrix specifying the digraph can be completed to a pi-matrix for pi either of the classes weakly sign symmetric P0,1-matrices, and sign symmetric P 0,1-matrices. Also, all symmetric digraphs of size 5 and 6 are classified as to completion for the class weakly sign symmetric P 0,1-matrices, and all symmetric digraphs of order 4 are classified for the class P0,1-matrices. A number of digraphs of size up through 4 are also classified as to whether or not every partial P0,1-matrix specifying the digraphs can be completed to a P0,1-matrix. A general result is proved that allows the assumption that the non-zero entries associated with up to n - 1 arcs of a subdigraph containing no semicycle are all equal to one in a partial matrix being completed.

dc.format.mimetype application/pdf dc.identifier archive/lib.dr.iastate.edu/rtd/1819/ dc.identifier.articleid 2818 dc.identifier.contextkey 6105695 dc.identifier.doi https://doi.org/10.31274/rtd-180813-12805 dc.identifier.s3bucket isulib-bepress-aws-west dc.identifier.submissionpath rtd/1819 dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/72086 dc.language.iso en dc.source.bitstream archive/lib.dr.iastate.edu/rtd/1819/r_3172251.pdf|||Fri Jan 14 21:38:07 UTC 2022 dc.subject.disciplines Mathematics dc.subject.keywords Mathematics dc.title The matrix completion problem regarding various classes of P0,1- matrices dc.type article dc.type.genre dissertation dspace.entity.type Publication relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48 thesis.degree.level dissertation thesis.degree.name Doctor of Philosophy
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