On the quasimonotonicity of a square linear operator with respect to a nonnegative cone
Approved for public release; distribution is unlimited === The question of when a square, linear operator is quasimonotone nondecreasing with respect to a nonnegative cone was posed for the application of vector Lyapunov functions in 1974. Necessary conditions were given in 1980, which were based on...
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Monterey, California. Naval Postgraduate School
2012
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| Online Access: | http://hdl.handle.net/10945/8768 |
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ndltd-nps.edu-oai-calhoun.nps.edu-10945-87682015-06-25T15:59:27Z On the quasimonotonicity of a square linear operator with respect to a nonnegative cone Beaver, Philip Canright, David Applied Mathematics Approved for public release; distribution is unlimited The question of when a square, linear operator is quasimonotone nondecreasing with respect to a nonnegative cone was posed for the application of vector Lyapunov functions in 1974. Necessary conditions were given in 1980, which were based on the spectrum and the first eigenvector. This dissertation gives necessary and sufficient conditions for the case of the real spectrum when the first eigenvector is in the nonnegative orthant, and when the first eigenvector is in the boundary of the nonnegative orthant, it gives conditions based on the reducibility of the matrix. For the complex spectrum, in the presence of a positive first eigenvector the problem is shown to be equivalent to the irreducible nonnegative inverse eigenvalue problem 2012-08-09T19:22:42Z 2012-08-09T19:22:42Z 1998-06 Thesis http://hdl.handle.net/10945/8768 en_US Monterey, California. Naval Postgraduate School |
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NDLTD |
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en_US |
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NDLTD |
| description |
Approved for public release; distribution is unlimited === The question of when a square, linear operator is quasimonotone nondecreasing with respect to a nonnegative cone was posed for the application of vector Lyapunov functions in 1974. Necessary conditions were given in 1980, which were based on the spectrum and the first eigenvector. This dissertation gives necessary and sufficient conditions for the case of the real spectrum when the first eigenvector is in the nonnegative orthant, and when the first eigenvector is in the boundary of the nonnegative orthant, it gives conditions based on the reducibility of the matrix. For the complex spectrum, in the presence of a positive first eigenvector the problem is shown to be equivalent to the irreducible nonnegative inverse eigenvalue problem |
| author2 |
Canright, David |
| author_facet |
Canright, David Beaver, Philip |
| author |
Beaver, Philip |
| spellingShingle |
Beaver, Philip On the quasimonotonicity of a square linear operator with respect to a nonnegative cone |
| author_sort |
Beaver, Philip |
| title |
On the quasimonotonicity of a square linear operator with respect to a nonnegative cone |
| title_short |
On the quasimonotonicity of a square linear operator with respect to a nonnegative cone |
| title_full |
On the quasimonotonicity of a square linear operator with respect to a nonnegative cone |
| title_fullStr |
On the quasimonotonicity of a square linear operator with respect to a nonnegative cone |
| title_full_unstemmed |
On the quasimonotonicity of a square linear operator with respect to a nonnegative cone |
| title_sort |
on the quasimonotonicity of a square linear operator with respect to a nonnegative cone |
| publisher |
Monterey, California. Naval Postgraduate School |
| publishDate |
2012 |
| url |
http://hdl.handle.net/10945/8768 |
| work_keys_str_mv |
AT beaverphilip onthequasimonotonicityofasquarelinearoperatorwithrespecttoanonnegativecone |
| _version_ |
1716806488076320768 |