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Matrix Completion Problems

✍ Scribed by Glória Cravo

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
379 KB
Volume
430
Category
Article
ISSN
0024-3795

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✦ Synopsis

Throughout the last decades, several results have been published in the area of the so-called Matrix Completion Problems. In this paper, we survey several results in this field. In particular, we describe the possible eigenvalues, the characteristic polynomial, the invariant polynomials, or the number of nontrivial invariant polynomials of a square matrix, over a field, when some of its entries are prescribed and the others vary. Finally, we present our contribution, generalizing some of the previous cases, to an n × n matrix partitioned into k × k blocks, with entries in a field, when some of its blocks are prescribed and the others vary.

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An n × n matrix is called an N -matrix if all its principal minors are negative. In this paper, we are interested in the symmetric N -matrix completion problem, that is, when a partial symmetric N -matrix has a symmetric N -matrix completion. Here, we prove that a partial symmetric N -matrix has a s