Geodesic
Linear Maps on Hermitian Matrices: The Stabilizer of an Inertia Class
Canadian mathematical bulletin, Tome 28 (1985) no. 4, pp. 401-404

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Let T be a linear transformation acting on the space of n x n complex matrices. Let G(k) be the set of all hermitian matrices with k positive and n — k negative eigenvalues. Let T map some indefinite inertia class G(k) onto itself. We classify all such T. The possibilities are congruence, congruence followed by transposition, and, if n = 2k, it is possible that — T can be a congruence or a congruence followed by transposing. In other words, negation is an admissible transformation when n = 2k.
DOI : 10.4153/CMB-1985-048-7
Mots-clés : Hermitian matrix, inertia class, 15A21, 15A27 
Linear Maps on Hermitian Matrices: The Stabilizer of an Inertia Class. Canadian mathematical bulletin, Tome 28 (1985) no. 4, pp. 401-404. doi: 10.4153/CMB-1985-048-7
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     title = {Linear {Maps} on {Hermitian} {Matrices:} {The} {Stabilizer} of an {Inertia} {Class}},
     journal = {Canadian mathematical bulletin},
     pages = {401--404},
     year = {1985},
     volume = {28},
     number = {4},
     doi = {10.4153/CMB-1985-048-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-048-7/}
}
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