The NIEP
The nonnegative inverse eigenvalue problem (NIEP) asks which lists of $n$ complex numbers (counting multiplicity) occur as the eigenvalues of some $n$-by-$n$ entry-wise nonnegative matrix. The NIEP has a long history and is a known hard (perhaps the hardest in matrix analysis?) and sought after prob...
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| creator | Johnson, Charles R Marijuán, Carlos Paparella, Pietro Pisonero, Miriam |
| description | The nonnegative inverse eigenvalue problem (NIEP) asks which lists of $n$
complex numbers (counting multiplicity) occur as the eigenvalues of some
$n$-by-$n$ entry-wise nonnegative matrix. The NIEP has a long history and is a
known hard (perhaps the hardest in matrix analysis?) and sought after problem.
Thus, there are many subproblems and relevant results in a variety of
directions. We survey most work on the problem and its several variants, with
an emphasis on recent results, and include 130 references. The survey is
divided into: a) the single eigenvalue problems; b) necessary conditions; c)
low dimensional results; d) sufficient conditions; e) appending 0's to achieve
realizability; f) the graph NIEP's; g) Perron similarities; and h) the
relevance of Jordan structure. |
| doi_str_mv | 10.48550/arxiv.1703.10992 |
| format | Article |
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complex numbers (counting multiplicity) occur as the eigenvalues of some
$n$-by-$n$ entry-wise nonnegative matrix. The NIEP has a long history and is a
known hard (perhaps the hardest in matrix analysis?) and sought after problem.
Thus, there are many subproblems and relevant results in a variety of
directions. We survey most work on the problem and its several variants, with
an emphasis on recent results, and include 130 references. The survey is
divided into: a) the single eigenvalue problems; b) necessary conditions; c)
low dimensional results; d) sufficient conditions; e) appending 0's to achieve
realizability; f) the graph NIEP's; g) Perron similarities; and h) the
relevance of Jordan structure.</description><identifier>DOI: 10.48550/arxiv.1703.10992</identifier><language>eng</language><subject>Mathematics - Spectral Theory</subject><creationdate>2017-03</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1703.10992$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1703.10992$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Johnson, Charles R</creatorcontrib><creatorcontrib>Marijuán, Carlos</creatorcontrib><creatorcontrib>Paparella, Pietro</creatorcontrib><creatorcontrib>Pisonero, Miriam</creatorcontrib><title>The NIEP</title><description>The nonnegative inverse eigenvalue problem (NIEP) asks which lists of $n$
complex numbers (counting multiplicity) occur as the eigenvalues of some
$n$-by-$n$ entry-wise nonnegative matrix. The NIEP has a long history and is a
known hard (perhaps the hardest in matrix analysis?) and sought after problem.
Thus, there are many subproblems and relevant results in a variety of
directions. We survey most work on the problem and its several variants, with
an emphasis on recent results, and include 130 references. The survey is
divided into: a) the single eigenvalue problems; b) necessary conditions; c)
low dimensional results; d) sufficient conditions; e) appending 0's to achieve
realizability; f) the graph NIEP's; g) Perron similarities; and h) the
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complex numbers (counting multiplicity) occur as the eigenvalues of some
$n$-by-$n$ entry-wise nonnegative matrix. The NIEP has a long history and is a
known hard (perhaps the hardest in matrix analysis?) and sought after problem.
Thus, there are many subproblems and relevant results in a variety of
directions. We survey most work on the problem and its several variants, with
an emphasis on recent results, and include 130 references. The survey is
divided into: a) the single eigenvalue problems; b) necessary conditions; c)
low dimensional results; d) sufficient conditions; e) appending 0's to achieve
realizability; f) the graph NIEP's; g) Perron similarities; and h) the
relevance of Jordan structure.</abstract><doi>10.48550/arxiv.1703.10992</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Spectral Theory |
| title | The NIEP |
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