328 research outputs found
Remembering Leiba Rodman 1949–2015, at IWOTA 2015
No full textThe present article covers the contributions of the speakers at the memorial session “Remembering Leiba Rodman” at IWOTA 2015
Remembering Leiba Rodman 1949–2015, at IWOTA 2015
No full textThe present article covers the contributions of the speakers at the memorial session “Remembering Leiba Rodman” at IWOTA 2015.</p
Factorization in Weighted Wiener Matrix Algebras on Linearly Ordered Abelian Groups
No full textFactorizations of Wiener-Hopf type of elements of weighted Wiener algebras of continuous matrix-valued functions on a compact abelian group are studied. The factorizations are with respect to a fixed linear order in the character group (considered with the discrete topology). Among other results, it is proved that if a matrix function has a canonical factorization in
one such matrix Wiener algebra then it belongs to the connected component of the identity of the group of invertible elements in the algebra, and moreover, the factors of the canonical factorization depend continuously on the matrix function. In the scalar case, complete characterizations of canonical and noncanonical factorability are given in terms of abstract winding numbers. Wiener-Hopf equivalence of matrix functions with elements in weighted Wiener algebras is also discussed
Factorization of Block Triangular Matrix Functions in Wiener Algebras on Ordered Abelian Groups
No full textINVARIANT NEUTRAL SUBSPACES FOR HAMILTONIAN MATRICES ∗
No full textAbstract. 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)
Mihály Matrix Completions, Moments, and Sums of Hermitian Squares by Mihály Bakonyi and Hugo J. Woerdeman, Princeton Series in Applied Mathematics, Princeton University Press (2011). xii + 518 pp., Hardback, ISBN 978-0-691-12889-4.
No full textUnknow
Remarks on Lipschitz properties of matrix groups actions
No full textAbstractIt is proved that a large class of matrix group actions, including joint similarity and congruence-like actions, as well as actions of the type of matrix equivalence, have local Lipschitz property. Under additional hypotheses, global Lipschitz property is proved. These results are specialized and applied to obtain local Lipschitz property of canonical bases of matrices that are selfadjoint in an indefinite inner product. Real, complex, and quaternionic matrices are considered
Pairs of hermitian and skew-hermitian quaternionic matrices: Canonical forms and their applications
No full textAbstractCanonical forms are described for pairs of quaternionic matrices, or equivalently matrix pencils, where each one of the matrices is either hermitian or skew-hermitian, under strict equivalence and simultaneous congruence. Several applications are developed, including structure of selfadjoint and skew-adjoint matrices with respect to a regular sesquilinear quaternion valued form, or with respect to a regular skew-sesquilinear form. Another application gives canonical forms for quaternionic matrices under congruence
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