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Title: Simultaneously self-adjoint sets of 3 X 3 matrices
Authors: Buckley, Anita
Tomaž, Košir
Keywords: Simultaneously self-adjoint sets of matrices, matrix definiteness, determinantal representation, linear matrix inequalities.
Issue Date: 2015
Publisher: EUT Edizioni Università di Trieste
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
47 (2015)
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.
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/0049-4704/11221
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.47 (2015)

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