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1 results

  • Linear Maps on Hermitian Matrices: The Stabilizer of an Inertia Class

  • Charles R. Johnson, Stephen Pierce
  • Journal:
    Canadian Mathematical Bulletin / Volume 28 / Issue 4 / 01 December 1985
    Published online by Cambridge University Press:
    20 November 2018, pp. 401-404
    Print publication:
    01 December 1985
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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.