Ela Invariant Neutral Subspaces for Hamiltonian Matrices
نویسندگان
چکیده
Hamiltonian matrices with respect to a nondegenerate skewsymmetric or skewhermitian indefinite inner product in finite dimensional real, complex, or quaternion vector spaces are studied. Subspaces that are simultaneously invariant for the matrices and neutral in the indefinite inner product are of special interest. The dimension of maximal (by inclusion) such subspaces is identified in terms of the canonical forms and sign characteristics. Criteria for uniqueness of maximal invariant neutral subspaces are given. The important special case of invariant Lagrangian subspaces is treated separately. Comparisons are made between real, complex, and quaternion contexts; for example, for complex Hamiltonian matrices with respect to a nondegenerate skewhermitian inner product in a finite dimensional complex vector space, the (complex) dimension of (complex) maximal invariant neutral subspaces is compared to the (quaternion) dimension of (quaternion) maximal invariant neutral subspaces, and necessary and sufficient conditions are given for the two dimensions to coincide (this is not always the case).
منابع مشابه
Invariant neutral subspaces for Hamiltonian matrices
Hamiltonian matrices with respect to a nondegenerate skewsymmetric or skewhermitian indefinite inner product in finite dimensional real, complex, or quaternion vector spaces are studied. Subspaces that are simultaneously invariant for the matrices and neutral in the indefinite inner product are of special interest. The dimension of maximal (by inclusion) such subspaces is identified in terms of...
متن کاملEla Hyponormal Matrices and Semidefinite Invariant Subspaces in Indefinite Inner Products
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 e...
متن کاملEla Real and Complex Invariant Subspaces for Matrices Which Are H-positive Real in an Indefinite Inner Product Space
In this paper, the equivalence of the existence of unique real and complex A-invariant semidefinite subspaces for real H-positive real matrices are shown.
متن کاملStructured Condition Numbers for Invariant Subspaces
Invariant subspaces of structured matrices are sometimes better conditioned with respect to structured perturbations than with respect to general perturbations. Sometimes they are not. This paper proposes an appropriate condition number cS, for invariant subspaces subject to structured perturbations. Several examples compare cS with the unstructured condition number. The examples include block ...
متن کاملEla Minimal Distortion Problems for Classes of Unitary Matrices ∗
Given two chains of subspaces in C, the set of those unitary matrices is studied that map the subspaces in the first chain onto the corresponding subspaces in the second chain, and minimize the value ‖U − In‖ for various unitarily invariant norms ‖ · ‖ on Cn×n. In particular, a formula for the minimum value ‖U − In‖ is given, and the set of all the unitary matrices in the set attaining the mini...
متن کامل