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  4. Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics
  5. Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.47 (2015)
  6. Simultaneously self-adjoint sets of 3 X 3 matrices
 
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Simultaneously self-adjoint sets of 3 X 3 matrices

Buckley, Anita
•
Tomaž, Košir
2015
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ISSN
0049-4704
DOI
10.13137/0049-4704/11221
http://hdl.handle.net/10077/11221
  • Article

e-ISSN
2464-8728
Abstract
For a generic set M of 3x3 matrices over C we find necessary and sufficient conditions when A4 is simultaneously self-adjoint. Moreover, for a set of complex hermitian matrices we can tell if there exists a linear combination of matrices which is positive definite. Every M can be identified with a determinantal representation of a cubic hypersurface. This allows us to use the tools of algebraic geometry. The question of definiteness can be solved by using semidefinite programming.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
47 (2015)
Subjects
  • Simultaneously self-a...

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EUT Edizioni Università di Trieste
Languages
en
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