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On localization of the eigenvalues of matrices "close" to triangular ones

Year 2022, Volume: 51 Issue: 4, 1104 - 1107, 01.08.2022

Michael Gil'

https://doi.org/10.15672/hujms.995747

Abstract

We suggest a new bound for the eigenvalues of a matrix. For matrices which are "close" to triangular ones that bound is sharper than the well-known results, such as the Ostrowski theorem.

Keywords

matrices localization of eigenvalues Ostrowski theorem

References

  • [1] A. Brauer, Limits for the characteristic roots of a matrix. II: Applications to stochastic matrices, Duke Math. J. 14 (1), 21-26, 1947.
  • [2] M. Fiedler, F.J. Hall and R. Marsli, Gershgorin discs revisited, Linear Algebra Appl. 438 (1), 598-603, 2013.
  • [3] S.A. Gershgorin. Uber die abgrenzung der eigenwerte einer matrix, Bull. Acad. des Sci. URSS 6, 749-754, 1931.
  • [4] M.I. Gil, Perturbations of determinants of matrices, Linear Algebra and its Appl. 590, 235–242, 2020.
  • [5] Ch.R. Johnson, J.M. Peña and T. Szulc, Optimal Gershgorin style estimation of the largest singular value, II, Electron. J. Linear Algebra, 31, 679-685, 2016.
  • [6] C.K. Li and F. Zhang, Eigenvalue continuity and Gershgorin’s theorem, Electron. J. Linear Algebra 35, 619-625, 2019.
  • [7] M. Marcus and H. Minc, A Survey of Matrix Theory and Matrix Inequalities, Allyn and Bacon, Boston 1964.
  • [8] S. Milicević, V.R. Kostić, Lj. Cvetković and A. Miedlar, An implicit algorithm for computing the minimal Gershgorin set, Filomat, 33 (13), 4229-4238, 2019.
  • [9] A. Ostrowski, Uber die determinanten mit űberwiegender hauptdiagonale, Comment. Math. Helv. 10, 69-96, 1937.
  • [10] A. Ostrowski. Uber das nichtverschwinden einer klasse von determinanten und die lokalisierung der charakteristischen wurzeln von matrizen, Compositio Mathematica, 9, 209–226, 1951.

Year 2022, Volume: 51 Issue: 4, 1104 - 1107, 01.08.2022

Michael Gil'

https://doi.org/10.15672/hujms.995747

Abstract

References

  • [1] A. Brauer, Limits for the characteristic roots of a matrix. II: Applications to stochastic matrices, Duke Math. J. 14 (1), 21-26, 1947.
  • [2] M. Fiedler, F.J. Hall and R. Marsli, Gershgorin discs revisited, Linear Algebra Appl. 438 (1), 598-603, 2013.
  • [3] S.A. Gershgorin. Uber die abgrenzung der eigenwerte einer matrix, Bull. Acad. des Sci. URSS 6, 749-754, 1931.
  • [4] M.I. Gil, Perturbations of determinants of matrices, Linear Algebra and its Appl. 590, 235–242, 2020.
  • [5] Ch.R. Johnson, J.M. Peña and T. Szulc, Optimal Gershgorin style estimation of the largest singular value, II, Electron. J. Linear Algebra, 31, 679-685, 2016.
  • [6] C.K. Li and F. Zhang, Eigenvalue continuity and Gershgorin’s theorem, Electron. J. Linear Algebra 35, 619-625, 2019.
  • [7] M. Marcus and H. Minc, A Survey of Matrix Theory and Matrix Inequalities, Allyn and Bacon, Boston 1964.
  • [8] S. Milicević, V.R. Kostić, Lj. Cvetković and A. Miedlar, An implicit algorithm for computing the minimal Gershgorin set, Filomat, 33 (13), 4229-4238, 2019.
  • [9] A. Ostrowski, Uber die determinanten mit űberwiegender hauptdiagonale, Comment. Math. Helv. 10, 69-96, 1937.
  • [10] A. Ostrowski. Uber das nichtverschwinden einer klasse von determinanten und die lokalisierung der charakteristischen wurzeln von matrizen, Compositio Mathematica, 9, 209–226, 1951.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Michael Gil' 0000-0002-6404-9618

Publication Date August 1, 2022
Published in Issue Year 2022 Volume: 51 Issue: 4

Cite

APA Gil’, M. (2022). On localization of the eigenvalues of matrices "close" to triangular ones. Hacettepe Journal of Mathematics and Statistics, 51(4), 1104-1107. https://doi.org/10.15672/hujms.995747
AMA Gil’ M. On localization of the eigenvalues of matrices "close" to triangular ones. Hacettepe Journal of Mathematics and Statistics. August 2022;51(4):1104-1107. doi:10.15672/hujms.995747
Chicago Gil’, Michael. “On Localization of the Eigenvalues of Matrices ‘close’ to Triangular Ones”. Hacettepe Journal of Mathematics and Statistics 51, no. 4 (August 2022): 1104-7. https://doi.org/10.15672/hujms.995747.
EndNote Gil’ M (August 1, 2022) On localization of the eigenvalues of matrices "close" to triangular ones. Hacettepe Journal of Mathematics and Statistics 51 4 1104–1107.
IEEE M. Gil’, “On localization of the eigenvalues of matrices ‘close’ to triangular ones”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 4, pp. 1104–1107, 2022, doi: 10.15672/hujms.995747.
ISNAD Gil’, Michael. “On Localization of the Eigenvalues of Matrices ‘close’ to Triangular Ones”. Hacettepe Journal of Mathematics and Statistics 51/4 (August 2022), 1104-1107. https://doi.org/10.15672/hujms.995747.
JAMA Gil’ M. On localization of the eigenvalues of matrices "close" to triangular ones. Hacettepe Journal of Mathematics and Statistics. 2022;51:1104–1107.
MLA Gil’, Michael. “On Localization of the Eigenvalues of Matrices ‘close’ to Triangular Ones”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 4, 2022, pp. 1104-7, doi:10.15672/hujms.995747.
Vancouver Gil’ M. On localization of the eigenvalues of matrices "close" to triangular ones. Hacettepe Journal of Mathematics and Statistics. 2022;51(4):1104-7.

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