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Volumn 302-303, Issue , 1999, Pages 105-133

Bezoutians of rational matrix functions, matrix equations and factorizations

Author keywords

Bezoutians; Factorization; Rational matrix functions; Realization

Indexed keywords


EID: 0033275142     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(99)00068-3     Document Type: Article
Times cited : (6)

References (54)
  • 1
    • 0016988383 scopus 로고
    • Generalized Bezoutian and Sylvester matrices in multivariable linear control
    • B.D.O. Anderson, E.I. Jury, Generalized Bezoutian and Sylvester matrices in multivariable linear control, IEEE Trans. Automat. Control AC-21 (1976) 551-556.
    • (1976) IEEE Trans. Automat. Control , vol.AC-21 , pp. 551-556
    • Anderson, B.D.O.1    Jury, E.I.2
  • 3
    • 0001645519 scopus 로고
    • Common minimal divisors and multiples for rational matrix functions
    • J.A. Ball, I. Gohberg, L. Rodman, Common minimal divisors and multiples for rational matrix functions, Linear Algebra and Appl. 137-138 (1990) 621-662.
    • (1990) Linear Algebra and Appl. , vol.137-138 , pp. 621-662
    • Ball, J.A.1    Gohberg, I.2    Rodman, L.3
  • 5
    • 0023305816 scopus 로고
    • Optimal Hankel norm model reductions and Wiener Hopf factorization I: The canonical case
    • J.A. Ball, A.C.M. Ran, Optimal Hankel norm model reductions and Wiener Hopf factorization I: The canonical case, SIAM J. Control and Optimization 25 (1987) 362-382.
    • (1987) SIAM J. Control and Optimization , vol.25 , pp. 362-382
    • Ball, J.A.1    Ran, A.C.M.2
  • 10
    • 0011473429 scopus 로고
    • On the effective computation of the inertia of a non-hermitian matrix
    • D. Carlson, B.N. Datta, On the effective computation of the inertia of a non-hermitian matrix, Numer. Math. 33 (1979) 315-322.
    • (1979) Numer. Math. , vol.33 , pp. 315-322
    • Carlson, D.1    Datta, B.N.2
  • 11
    • 0011401763 scopus 로고
    • Note sur la méthode d'élimination de Bézout
    • A. Cayley, Note sur la méthode d'élimination de Bézout., J. Reine Angew. Math. 539 (1857) 366-376.
    • (1857) J. Reine Angew. Math. , vol.539 , pp. 366-376
    • Cayley, A.1
  • 13
    • 0000775205 scopus 로고
    • The Bezoutian and the algebraic Riccati equation
    • K. Clancey, B.A. Kon, The Bezoutian and the algebraic Riccati equation, Linear and Multilinear Algebra 15 (1984) 265-278.
    • (1984) Linear and Multilinear Algebra , vol.15 , pp. 265-278
    • Clancey, K.1    Kon, B.A.2
  • 14
    • 0011406771 scopus 로고
    • On the Routh-Hurwitz-Fujiwara and the Schur-Cohn-Fujiwara theorems for the root-separation problem
    • B.N. Datta, On the Routh-Hurwitz-Fujiwara and the Schur-Cohn-Fujiwara theorems for the root-separation problem, Linear Algebra and Appl. 22 (1978) 235-246.
    • (1978) Linear Algebra and Appl. , vol.22 , pp. 235-246
    • Datta, B.N.1
  • 16
    • 0009976701 scopus 로고
    • On algebraic equations whose roots lie in a circle or in a half-plane
    • In German
    • M. Fujiwara, On algebraic equations whose roots lie in a circle or in a half-plane, Math. Zeitschrift 24 (1926) 161-169 [In German].
    • (1926) Math. Zeitschrift , vol.24 , pp. 161-169
    • Fujiwara, M.1
  • 18
    • 0000493451 scopus 로고
    • Common multiples and common divisors of operator polynomials, I. Spectral method
    • I. Gohberg, M.A. Kaashoek, L. Lerer, L. Rodman, Common multiples and common divisors of operator polynomials, I. Spectral method, Indiana Journal of Mathematics 30 (1981) 321-356.
    • (1981) Indiana Journal of Mathematics , vol.30 , pp. 321-356
    • Gohberg, I.1    Kaashoek, M.A.2    Lerer, L.3    Rodman, L.4
  • 23
    • 0000201706 scopus 로고
    • An operator generalization of the logarithmic residue theorem and Rouche's theorem
    • I. Gohberg, E.I. Sigal, An operator generalization of the logarithmic residue theorem and Rouche's theorem, Matem. Sbornik 84 (126) (1971) 607-629. English transl.: Math. USSR Sbornik 13 (1971) 603-625.
    • (1971) Matem. Sbornik , vol.84 , Issue.126 , pp. 607-629
    • Gohberg, I.1    Sigal, E.I.2
  • 24
    • 84956263391 scopus 로고
    • English transl.
    • I. Gohberg, E.I. Sigal, An operator generalization of the logarithmic residue theorem and Rouche's theorem, Matem. Sbornik 84 (126) (1971) 607-629. English transl.: Math. USSR Sbornik 13 (1971) 603-625.
    • (1971) Math. USSR Sbornik , vol.13 , pp. 603-625
  • 25
    • 0002899727 scopus 로고
    • Bezout operators for analytic operator functions. I. a general concept of Bezout operators
    • J. Haimovici, L. Lerer, Bezout operators for analytic operator functions. I. A general concept of Bezout operators, Integral Equations and Operator Theory 21 (1995) 33-70.
    • (1995) Integral Equations and Operator Theory , vol.21 , pp. 33-70
    • Haimovici, J.1    Lerer, L.2
  • 27
    • 0012031958 scopus 로고
    • Nonsingular solutions of TA - BT = C
    • J.Z. Hearon, Nonsingular solutions of TA - BT = C, Linear Algebra and Appl. 16 (1977) 57-65.
    • (1977) Linear Algebra and Appl. , vol.16 , pp. 57-65
    • Hearon, J.Z.1
  • 28
    • 21844498182 scopus 로고
    • Matrix representations of Bezoutians
    • G. Heinig, Matrix representations of Bezoutians, Linear Algebra and Appl. 223 (1995) 337-354.
    • (1995) Linear Algebra and Appl. , vol.223 , pp. 337-354
    • Heinig, G.1
  • 31
    • 0011452575 scopus 로고
    • Sur le nombre des racines d'une équation algébrique comprise entre des limites donnés
    • C. Hermite, Sur le nombre des racines d'une équation algébrique comprise entre des limites donnés, J. Reine Angew. Math. 52 (1856) 39-51.
    • (1856) J. Reine Angew. Math. , vol.52 , pp. 39-51
    • Hermite, C.1
  • 32
    • 0011499023 scopus 로고
    • On the Hermite-Fujiwara theorem in stability theory
    • R.E. Kalman, On the Hermite-Fujiwara theorem in stability theory, Quart. Appl. Math. 23 (1965) 279-282.
    • (1965) Quart. Appl. Math. , vol.23 , pp. 279-282
    • Kalman, R.E.1
  • 33
    • 0002917393 scopus 로고
    • On eigenvalues and eigenfunctions of some classes of nonselfadjoint equations
    • in Russian
    • M.V. Keldysh, On eigenvalues and eigenfunctions of some classes of nonselfadjoint equations, Doklady AN SSSR 77 (1951) 11-14 (in Russian).
    • (1951) Doklady AN SSSR , vol.77 , pp. 11-14
    • Keldysh, M.V.1
  • 35
    • 0002225475 scopus 로고
    • M.G. Krein, M.A. Naimark, The method of symmetric and hermitian forms in theory of separation of the roots of algebraic equations, GNTI, Kharkov, 1936 (Russian); Linear and Multilinear Algebra 10 (1981) 265-308.
    • (1981) Linear and Multilinear Algebra , vol.10 , pp. 265-308
  • 36
    • 0039616737 scopus 로고
    • Factored form of solutions of the equation AX-XB = C in companion matrices
    • P. Lancaster, L. Lerer, M. Tismenetsky, Factored form of solutions of the equation AX-XB = C in companion matrices, Linear Algebra and Appl. 62 (1984) 19-49.
    • (1984) Linear Algebra and Appl. , vol.62 , pp. 19-49
    • Lancaster, P.1    Lerer, L.2    Tismenetsky, M.3
  • 37
    • 0001062621 scopus 로고
    • The kernel of the Bezoutian for operator polynomials
    • P. Lancaster, J. Maroulas, The kernel of the Bezoutian for operator polynomials, Linear and Multilinear Algebra 17 (1985) 181-201.
    • (1985) Linear and Multilinear Algebra , vol.17 , pp. 181-201
    • Lancaster, P.1    Maroulas, J.2
  • 39
    • 0002674346 scopus 로고
    • The matrix quadratic equations and factorization of matrix polynomials
    • L. Lerer, The matrix quadratic equations and factorization of matrix polynomials, Operator Theory: Advances and Applications 40 (1989) 279-324.
    • (1989) Operator Theory: Advances and Applications , vol.40 , pp. 279-324
    • Lerer, L.1
  • 40
    • 0040653955 scopus 로고    scopus 로고
    • J-pseudo-spectral and J-inner-pseudo-outer factorizations for matrix polynomials
    • L. Lerer, A.C.M. Ran, J-pseudo-spectral and J-inner-pseudo-outer factorizations for matrix polynomials, Integral Equations and Operator Theory 29 (1997) 23-51.
    • (1997) Integral Equations and Operator Theory , vol.29 , pp. 23-51
    • Lerer, L.1    Ran, A.C.M.2
  • 41
    • 38249009842 scopus 로고
    • Spectrum separation and inertia for operator polynomials
    • L. Lerer, L. Rodman, Spectrum separation and inertia for operator polynomials, J. Math. Anal and Appl. 169 (1992) 260-282.
    • (1992) J. Math. Anal and Appl. , vol.169 , pp. 260-282
    • Lerer, L.1    Rodman, L.2
  • 42
    • 38249001334 scopus 로고
    • Sylvester and Lyapunov equations and some interpolation problems for rational matrix functions
    • L. Lerer, L. Rodman, Sylvester and Lyapunov equations and some interpolation problems for rational matrix functions, Linear Algebra and Appl. 185 (1993) 83-117.
    • (1993) Linear Algebra and Appl. , vol.185 , pp. 83-117
    • Lerer, L.1    Rodman, L.2
  • 43
    • 0346476049 scopus 로고
    • Bezoutians and factorizations of rational matrix functions and matrix equations
    • U. Helmke, R. Mennicken, J. Saurer (Eds.), Akademie Verlag
    • L. Lerer, L. Rodman, Bezoutians and factorizations of rational matrix functions and matrix equations, in: U. Helmke, R. Mennicken, J. Saurer (Eds.), Systems and Networks: Mathematical Theory and Applications, Akademie Verlag, 1994, pp. 761-766.
    • (1994) Systems and Networks: Mathematical Theory and Applications , pp. 761-766
    • Lerer, L.1    Rodman, L.2
  • 44
    • 0347736725 scopus 로고
    • Inertia of operator polynomials and stability of differential equations
    • L. Lerer, L. Rodman, Inertia of operator polynomials and stability of differential equations, J. Math. Anal. and Appl. 192 (1995) 579-606.
    • (1995) J. Math. Anal. and Appl. , vol.192 , pp. 579-606
    • Lerer, L.1    Rodman, L.2
  • 45
    • 0030579030 scopus 로고    scopus 로고
    • Bezoutians of rational matrix functions
    • L. Lerer, L. Rodman, Bezoutians of rational matrix functions, J. Functional Anal. 141 (1996) 1-36.
    • (1996) J. Functional Anal. , vol.141 , pp. 1-36
    • Lerer, L.1    Rodman, L.2
  • 46
    • 0030600690 scopus 로고    scopus 로고
    • Common zero structure of rational matrix functions
    • L. Lerer, L. Rodman, Common zero structure of rational matrix functions, J. Func. Anal. 136 (1996) 1-38.
    • (1996) J. Func. Anal. , vol.136 , pp. 1-38
    • Lerer, L.1    Rodman, L.2
  • 47
    • 0040206276 scopus 로고    scopus 로고
    • Symmetric factorizations and localization of zeroes of rational matrix functions
    • L. Lerer, L. Rodman, Symmetric factorizations and localization of zeroes of rational matrix functions, Linear and Multilinear Algebra 40 (1996) 259-281.
    • (1996) Linear and Multilinear Algebra , vol.40 , pp. 259-281
    • Lerer, L.1    Rodman, L.2
  • 48
    • 0021505269 scopus 로고
    • Bezoutian and the Schur-Cohn problem for operator polynomials
    • L. Lerer, L. Rodman, M. Tismenetsky, Bezoutian and the Schur-Cohn problem for operator polynomials, J. Math. Anal. Appl. 103 (1984) 83-102.
    • (1984) J. Math. Anal. Appl. , vol.103 , pp. 83-102
    • Lerer, L.1    Rodman, L.2    Tismenetsky, M.3
  • 50
    • 34250231929 scopus 로고
    • The Bezoutian and eigenvalue separation problem for matrix polynomials
    • L. Lerer, M. Tismenetsky, The Bezoutian and eigenvalue separation problem for matrix polynomials, Integral Equations and Operator Theory 5 (1982) 386-445.
    • (1982) Integral Equations and Operator Theory , vol.5 , pp. 386-445
    • Lerer, L.1    Tismenetsky, M.2
  • 51
    • 0011405169 scopus 로고
    • Generalized Bezoutian and matrix equations
    • L. Lerer, M. Tismenetsky, Generalized Bezoutian and matrix equations, Linear Algebra and Appl. 99 (1988) 123-160.
    • (1988) Linear Algebra and Appl. , vol.99 , pp. 123-160
    • Lerer, L.1    Tismenetsky, M.2
  • 52
    • 0041143291 scopus 로고
    • Invertible solutions to the operator equation TA - BT = C
    • D.G. Luenberger, Invertible solutions to the operator equation TA - BT = C, Proc. Amer. Math. Soc. 16 (1965) 1226-1229.
    • (1965) Proc. Amer. Math. Soc. , vol.16 , pp. 1226-1229
    • Luenberger, D.G.1
  • 53
    • 0001453534 scopus 로고
    • On a theory of syzygetic relations of two rational integral functions, comprising an application to the theory of Sturm's functions, and that of the greatest algebraic common measure
    • J.J. Sylvester, On a theory of syzygetic relations of two rational integral functions, comprising an application to the theory of Sturm's functions, and that of the greatest algebraic common measure, Philos. Trans. Roy. Soc. London 143 (1853) 407-548.
    • (1853) Philos. Trans. Roy. Soc. London , vol.143 , pp. 407-548
    • Sylvester, J.J.1
  • 54
    • 0011405387 scopus 로고
    • On the history of the Bezoutian and the resultant matrix
    • H.K. Wimmer, On the history of the Bezoutian and the resultant matrix, Linear Algebra and Appl. 128 (1990) 27-34.
    • (1990) Linear Algebra and Appl. , vol.128 , pp. 27-34
    • Wimmer, H.K.1


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