Geodesic
Neutral subspaces of pairs of symmetric/skewsymmetric real matrices
The electronic journal of linear algebra, Tome 22 (2011), pp. 979-999.

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

Summary: Let A and B be n $\times n$ real matrices with A symmetric and B skewsymmetric. Obviously, every simultaneously neutral subspace for the pair (A, B) is neutral for each Hermitian matrix X of the form $X = \mu A + i\lambda B$, where $\mu $and $\lambda $are arbitrary real numbers. It is well-known that the dimension of each neutral subspace of X is at most In + (X) + In 0 (X), and similarly, the dimension of each neutral subspace of X is at most In - (X) + In 0 (X). These simple observations yield that the maximal possible dimension of an (A, B)-neutral subspace is no larger than $min{min{In + (\mu A + i\lambda B) + In 0 (\mu A + i\lambda B)$, In - $(\mu A + i\lambda B) + In 0 (\mu A + i\lambda B)}}$, where the outer minimum is taken over all pairs of real numbers $(\lambda , \mu )$. In this paper, it is proven that the maximal possible dimension of an (A, B)-neutral subspace actually coincides with the above expression.
Classification : 15A21, 15A22, 15B57
Keywords: symmetric matrix, skewsymmetric matrix, Hermitian matrix, inertia, neutral subspace 
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     title = {Neutral subspaces of pairs of symmetric/skewsymmetric real matrices},
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Rodman, Leiba; Semrl, Peter. Neutral subspaces of pairs of symmetric/skewsymmetric real matrices. The electronic journal of linear algebra, Tome 22 (2011), pp. 979-999. http://geodesic.mathdoc.fr/item/ELA_2011__22__a14/