Canonical forms for symmetric/skew-symmetric real matrix pairs under strict equivalence and congruence

[1]  H. W. Turnbull,et al.  An Introduction to the Theory of Canonical Matrices , 1932, Nature.

[2]  R. C. Thompson,et al.  The characteristic polynomial of a principal subpencil of a Hermitian matrix pencil , 1976 .

[3]  Leiba Rodman,et al.  Stable Invariant Lagrangian Subspaces: Factorization of Symmetric Rational Matrix Functions and Other Applications , 1990 .

[4]  V. Mehrmann,et al.  Structured Jordan canonical forms for structured matrices that are hermitian, skew hermitian or unitary with respect to indefinite inner products , 1999 .

[5]  F. Gantmacher,et al.  Applications of the theory of matrices , 1960 .

[6]  Leiba Rodman,et al.  Canonical Forms for Hermitian Matrix Pairs under Strict Equivalence and Congruence , 2005, SIAM Rev..

[7]  P. Lancaster,et al.  Invariant subspaces of matrices with applications , 1986 .

[8]  John Williamson.  The Equivalence of Non-Singular Pencils of Hermitian Matrices in an Arbitrary Field , 1935 .

[9]  N. Burgoyne,et al.  Normal forms for real linear Hamiltonian systems with purely imaginary eigenvalues , 1974 .

[10]  Richard A. Silverman,et al.  An introduction to the theory of linear spaces , 1963 .

[11]  Mark A. Shayman,et al.  Geometry of the Algebraic Riccati Equation, Part II , 1983 .

[12]  J. Rubin,et al.  Direct complements of invariant lagrangian subspaces and minimal factorizations of skew-symmetric rational matrix functions , 1993 .

[13]  K. Venkatachaliengar.  Pairs of symmetric and skew matrices in an arbitrary field—I , 1945 .

[14]  P. Lancaster,et al.  Invariant Neutral Subspaces for Symmetric and Skew Real Matrix Pairs , 1994, Canadian Journal of Mathematics.

[15]  J. Williamson.  The Conjunctive Equivalence of Pencils of Hermitian and Anti-Hermitian Matrices , 1937 .

[16]  L. Mirsky,et al.  The Theory of Matrices , 1961, The Mathematical Gazette.

[17]  T. C. Brown,et al.  Foundations of Linear Algebra. , 1968 .

[18]  Jiří Patera,et al.  Normal forms of elements of classical real and complex Lie and Jordan algebras , 1983 .

[19]  M. H. Ingraham,et al.  The equivalence of pairs of Hermitian matrices , 1935 .

[20]  Leiba Rodman,et al.  Matrices and indefinite scalar products , 1983 .

[21]  Loo-Keng Hua,et al.  On the Theory of Automorphic Functions of a Matrix Variable, II-The Classification of Hypercircles Under the Symplectic Group , 1944 .

[22]  H. W. Turnbull.  On the Equivalence of Pencils of Hermitian Forms , 1935 .

[23]  Christian Mehl,et al.  Condensed Forms for Skew-Hamiltonian/Hamiltonian Pencils , 1999, SIAM J. Matrix Anal. Appl..

[24]  J. Dieudonné,et al.  Sur la réduction canonique des couples de matrices , 1946 .

[25]  G. Richard Trott.  On the Canonical Form of a Non-Singular Pencil of Hermitian Matrices , 1934 .

[26]  K. Meyer,et al.  Canonical forms for symplectic and Hamiltonian matrices , 1974 .

[27]  W. Greub.  Linear Algebra , 1981 .

[28]  Wilhelm Kltngenberg.  Paare symmetrischer und alternierender formen zweiten grades , 1954 .

[29]  Volker Mehrmann,et al.  Canonical forms for Hamiltonian and symplectic matrices and pencils , 1999 .

[30]  P. Lancaster,et al.  Existence and uniqueness theorems for the algebraic Riccati equation , 1980 .

[31]  Leiba Rodman,et al.  Stability of Invariant Lagrangian Subspaces II , 1989 .

[32]  R. Coleman.  Some Properties of Elementary Hamiltonian Matrices , 2002 .

[33]  Martin Kummer,et al.  A Unified Approach to Linear and Nonlinear Normal Forms for Hamiltonian Systems , 1999, J. Symb. Comput..

[34]  Realization and Factorization for Rational Matrix Functions with Symmetries , 1990 .

[35]  R. C. Thompson,et al.  Pencils of complex and real symmetric and skew matrices , 1991 .

[36]  L. Rodman,et al.  A class of robustness problems in matrix analysis , 2002 .

[37]  Vladimir V. Sergeichuk,et al.  Canonical matrices for linear matrix problems , 2000, 0709.2485.

[38]  A. Bryuno.  The normal form of a Hamiltonian system , 1988 .

[39]  Leiba Rodman,et al.  Algebraic Riccati equations , 1995 .

[40]  V. Mehrmann,et al.  Canonical forms for doubly structured matrices and pencils , 2000 .

[41]  John Williamson.  Note on the equivalence of nonsingular pencils of Hermitian matrices , 1945 .

[42]  H. W. Turnbull,et al.  Lectures on Matrices , 1934 .

[43]  L. E. Faibusovich.  Algebraic Riccati equation and symplectic algebra , 1986 .

[44]  Peter Benner,et al.  Numerical Computation of Deflating Subspaces of Skew-Hamiltonian/Hamiltonian Pencils , 2002, SIAM J. Matrix Anal. Appl..

[45]  C. C. Macduffee,et al.  The Theory of Matrices , 1933 .

[46]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[47]  P. Fuhrmann.  On Hamiltonian rational transfer functions , 1984 .

[48]  Leiba Rodman,et al.  Minimal symmetric factorizations of symmetric real and complex rational matrix functions , 1995 .

[49]  C. Loan,et al.  A Schur decomposition for Hamiltonian matrices , 1981 .

[50]  David S. Watkins,et al.  On Hamiltonian and symplectic Lanczos processes , 2004 .

[51]  J. Williamson.  On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems , 1936 .

[52]  Niloufer Mackey,et al.  Hamiltonian square roots of skew-Hamiltonian matrices , 1999 .

[53]  Peter Benner,et al.  A NOTE ON THE NUMERICAL SOLUTION OF COMPLEX HAMILTONIAN AND SKEW-HAMILTONIAN EIGENVALUE PROBLEMS , 1999 .