Skip to main content
SpringerLink
Log in

Inverse matrix eigenvalue problems

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. F. R. Gantmakher,Matrix Theory [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  2. Kh. D. Ikramov, “On the arrangement of poles of linear stationry systems,”Vychisl. Protsessy, Systemy,9, 35–162 (1993).

    MATH  MathSciNet  Google Scholar 

  3. Kh. D. Ikramov and C. Williamson, “On the Hegland-Marty inverse eigenvalue problem,”Mat. Zametki,61, 1, 144–148 (1977).

    MathSciNet  Google Scholar 

  4. Kh. D. Ikramov and V. N. Chugunov, “Rational solvability of the Silva inverse problem,”Zh. Vychisl. Mat. Mat. Fiz.,36, 6, 20–27 (1996).

    MathSciNet  Google Scholar 

  5. M. G. Krein and M. A. Naimark,Method of Symmetric and Hermitian Forms in the Theory of Separation of Roots of Algebraic Equations [in Russian], Khar'kov (1936).

  6. M. Marcus and H. Minc,A Survey of Matrix Theory and Matrix Inequalities [Russian translation], Nauka, Moscow (1972).

    Google Scholar 

  7. B. Parlett,The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, New Jersey (1980).

    Google Scholar 

  8. R. Horn and C. Johnson,Matrix Analysis [Russian transl.], Mir, Moscow (1989).

    Google Scholar 

  9. V. N. Chugunov, “On the transformation of a matrix into a matrix with a given principal diagonal via a similarity transformation,” In:Applied Programs Packages [in Russian], Moscow State University Press, Moscow (1997), pp. 133–140.

    Google Scholar 

  10. J. Barŕia and P. R. Halmos, “Weakly transitive matrices,”Ill. J. Math.,28, 370–378 (1984).

    Google Scholar 

  11. H. K. Farahat and W. Ledermann, “Matrices with prescribed characteristic polynomials,”Proc. Edinburgh Math. Soc.,11, 143–146 (1958).

    MathSciNet  Google Scholar 

  12. M. Fiedler, “Expressing a polynomial as the characteristic polynomial of a symmetric matrix,”Linear Algebra Appl.,14, 255–270 (1990).

    Google Scholar 

  13. P. A. Fillmore, “On similarity and the diagonal of a matrix,”Amer. Math. Monthly,76, 167–169 (1969).

    MATH  MathSciNet  Google Scholar 

  14. S. Friedland, “Inverse eigenvalue problems,”Linear Algebra Appl.,17, 15–51 (1977).

    Article  MATH  MathSciNet  Google Scholar 

  15. S. Friedland, “Matrices with prescribed off-diagonal elements,”Isr. J. Math.,11, 184–189 (1972).

    MATH  MathSciNet  Google Scholar 

  16. A. George A., Kh. D. Ikramov, A. N. Krivoshapova, and W.-P. Tang, “A finite procedure for the tridiagonalization of a general matrix,”SIAM J. Matrix Anal. Appl.,16, 2, 377–387 (1995).

    Article  MathSciNet  Google Scholar 

  17. A. George, Kh. D. Ikramov, W. P. Tang, and V. N. Chugunov, “On the double symmetric tridiagonal form for complex matrices and tridiagonal inverse eigenvalue problems,”SIAM J. Matrix Anal. Appl.,17, No. 3, 680–690 (1996).

    MathSciNet  Google Scholar 

  18. D. Hershkowitz, “Existence of matrices with prescribed eigenvalues and entries,”Linear Multilinear Algebra,14, 315–342 (1983).

    MATH  MathSciNet  Google Scholar 

  19. S.-A. Hu and E. Spiegel, “The similarity class of a matrix,”Linear Algebra Appl.,233, 231–241 (1996).

    Article  MathSciNet  Google Scholar 

  20. Kh. D. Ikramov and V. N. Chugunov, “On the Teng inverse eigenvalue problem,”Linear Algebra Appl.,208/209, 397–399 (1994).

    Article  MathSciNet  Google Scholar 

  21. C. R. Johnson, C.-K. Li, L. Rodman, I. Spitkovsky, and S. Pierce, “Linear maps preserving regional eigenvalue location,”Linear Multilinear Algebra,32, 3/4, 253–264 (1992).

    MathSciNet  Google Scholar 

  22. C. R. Johnson and H. Shapiro, “Mathematical aspects of the relative gain array [AA −t]*,”SIAM J. Alg. Discr. Math.,7, 4, 627–644 (1986).

    MathSciNet  Google Scholar 

  23. D. London and H. Minc, “Eigenvalues of matries with prescribed entries,”Proc. Amer. Math. Soc.,34, 8–14 (1972).

    MathSciNet  Google Scholar 

  24. M. G. Marques and F. C. Silva, “The characteristic polynomial of a matrix with prescribed off-diagonal blocks,”Linear Algebra Appl.,250, 21–29 (1997).

    Article  MathSciNet  Google Scholar 

  25. M. G. Marques, F. C. Silva, and Z. Y. Lin, “The number of invariant polynomials of a matrix with prescribed complementary principal submatrices,”Linear Algebra Appl.,251, 167–179 (1997).

    MathSciNet  Google Scholar 

  26. M. G. Marques, “The number of invariant polynomials of a matrix with prescribed off-diagonal blocks,”Linear Algebra Appl.,258, 149–158 (1997).

    MATH  MathSciNet  Google Scholar 

  27. L. Mirsky, “Matrices with prescribed characteristic roots and diagonal elements,”J. London Math. Soc.,33, 14–21 (1958).

    MATH  MathSciNet  Google Scholar 

  28. G. N. de Oliveira, “Matrices with prescribed characteristic polynomial and a prescribed submatrix, III,”Monatsh. Math.,75, 441–446 (1971).

    Article  MATH  MathSciNet  Google Scholar 

  29. G. N. de Oliveira, “Matrices with prescribed entries and eigenvalues. I,”Proc. Amer. Math. Soc.,37, 380–386 (1973).

    MATH  MathSciNet  Google Scholar 

  30. G. N. de Oliveira, “Matrices with prescribed entries and eigenvalues. II,”SIAM J. Appl. Math.,24, 414–417 (1973).

    MATH  MathSciNet  Google Scholar 

  31. G. N. de Oliveira, “Matrices with prescribed entries and eigenvalues. III,”Arch. Math. 26, 57–59 (1975).

    Article  MATH  Google Scholar 

  32. G. N. de Oliveira, “Matrices with prescribed submatrices,”Linear Multilinear Algebra,12, 125–138 (1982).

    MATH  Google Scholar 

  33. G. N. de Oliveira, E. M. de Sá, and J. A. D. da Silva, “On the eigenvalues of the matrixA+XBX −1,”Linear Multilinear Algebra,5, 119–128 (1977).

    Google Scholar 

  34. G. N. de Oliveria, “The characteristic values of the matrixA+XBX −1,” In:Proc. Coll. Numerical Methods, Keszthely, Hungary (1977), pp. 491–500.

  35. E. M. de Sá, “Imbedding conditions for λ-matrices,”Linear Algebra Appl.,24, 33–50 (1979).

    MATH  MathSciNet  Google Scholar 

  36. G. Schmeiser, “A real symmetric tridiagonal matrix with a given characteristic polynomial,”Linear Algebra Appl.,193, 11–18 (1973).

    Google Scholar 

  37. F. C. Silva, “Matrices with prescribed lower triangular part,”Linear Algebra Appl.,182, 27–34 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  38. F. C. Silva, “Matrices with prescribed characteristic polynomial and submatrices,”Portugal. Math.,44, 261–264 (1987).

    MATH  MathSciNet  Google Scholar 

  39. F. C. Silva, “Matrices with prescribed eigenvalues and blocks,”Linear Algebra Appl.,148, 59–73 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  40. F. C. Silva, “Matrices with prescribed eigenvalues and principal submatrices,”Linear Algebra Appl.,92, 241–250 (1987).

    MATH  MathSciNet  Google Scholar 

  41. J. A. D. da Silva, “Matrices with prescribed entries and characteristic polynomial,”Proc. Amer. Math. Soc.,45, 31–37 (1974).

    MATH  MathSciNet  Google Scholar 

  42. K. Takahashi, “Eigenvalues of matrices with given block upper triangular part,”Linear Algebra Appl.,239, 175–184 (1996).

    MATH  MathSciNet  Google Scholar 

  43. R. C. Thompson, “Interlacing inequalities for invariant factors,”Linear Algebra Appl.,24, 1–31 (1979).

    Article  MATH  MathSciNet  Google Scholar 

  44. H. K. Wimmer, “Existenzsätze in der Theorie der Matrizen und linear Kontrolltheorie,”Monatsh. Math.,78, 256–263 (1974).

    Article  MATH  MathSciNet  Google Scholar 

  45. W. M. Wonham and A. S. Morse, “Decoupling and pole assignment in linear multivariable systems: a geometric approach,”SIAM J. Control,8, 1–18 (1970).

    Article  MathSciNet  Google Scholar 

  46. I. Zaballa, “Existence of matrices with prescribed entries,”Linear Algebra Appl.,73, 227–280 (1986).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Authors
  1. Kh. D. Ikramov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. N. Chugunov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya, Tematicheskie Obzory. Vol. 52, Algebra-9, 1998.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ikramov, K.D., Chugunov, V.N. Inverse matrix eigenvalue problems. J Math Sci 98, 51–136 (2000). https://doi.org/10.1007/BF02355380

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02355380

Keywords

Search

Navigation