Geodesic
Hyponormal matrices and semidefinite invariant subspaces in indefinite inner products
The electronic journal of linear algebra, Tome 11 (2004), pp. 192-204.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: It is shown that, for any given polynomially normal matrix with respect to an indefinite inner product, a nonnegative (with respect to the indefinite inner product) invariant subspace always admits an extension to an invariant maximal nonnegative subspace. Such an extension property is known to hold true for general normal matrices if the nonnegative invariant subspace is actually neutral. An example is constructed showing that the extension property does not generally hold true for normal matrices, even when the nonnegative invariant subspace is assumed to be positive. On the other hand, it is proved that the extension property holds true for hyponormal (with respect to the indefinite inner product) matrices under certain additional hypotheses.
Classification : 15A63, 15A57
Keywords: indefinite inner products, semidefinite invariant subspaces, hyponormal matrices, normal matrices 
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     author = {Mehl, Christian and Ran, Andr\'e C.M. and Rodman, Leiba},
     title = {Hyponormal matrices and semidefinite invariant subspaces in indefinite inner products},
     journal = {The electronic journal of linear algebra},
     pages = {192--204},
     publisher = {mathdoc},
     volume = {11},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2004__11__a6/}
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Mehl, Christian; Ran, André C.M.; Rodman, Leiba. Hyponormal matrices and semidefinite invariant subspaces in indefinite inner products. The electronic journal of linear algebra, Tome 11 (2004), pp. 192-204. http://geodesic.mathdoc.fr/item/ELA_2004__11__a6/