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Simultaneously self-adjoint sets of 3 X 3 matrices
Buckley, Anita
Tomaž, Košir
2015
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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
Publisher
EUT Edizioni Università di Trieste
Languages
en
File(s)