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Research Article

Extremal inverse eigenvalue problem for irreducible acyclic matrices

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Pages 192-209 | Received 02 Apr 2021, Accepted 07 Feb 2022, Published online: 27 Feb 2022

References

  • Nair R, Shader BL. Acyclic matrices with a small number of distinct eigenvalues. Linear Algebra Appl. 2013;438(10):4075–4089. DOI: 10.1016/j.laa.2012.08.029.
  • Peng J, Hu X, Zhang L. Two inverse eigenvalue problems for a special kind of matrices. Linear Algebra Appl. 2006;416(2):336–347. DOI: 10.1016/j.laa.2005.11.017.
  • Soto RL, Pickmann H, Egana JC. Two inverse eigenproblems for symmetric doubly arrow matrices. Electron J Linear Algebra. 2009;18:700–718. DOI: 10.13001/1081-3810.1339.
  • Pickmann H, Egana J, Soto RL. Extremal inverse eigenvalue problem for bordered diagonal matrices. Linear Algebra Appl. 2007;427(2):256–271. DOI: 10.1016/j.laa.2007.07.020.
  • Sharma D, Sen M. Inverse eigenvalue problems for two special acyclic matrices. Mathematics. 2016;4(1):12. DOI: 10.3390/math4010012.
  • Xu W-R, Chen G-L. On inverse eigenvalue problems for two kinds of special banded matrices. Filomat. 2017;31(2):371–385. ISSN 03545180, 24060933.
  • Sharma D, Sen M. Inverse eigenvalue problems for acyclic matrices whose graph is a dense centipede. Special Matrices. 2018;6(1):77–92. DOI: 10.1515/spma-2018-0008.
  • Heydari M, Fazeli SAS, Karbassi SM. On the inverse eigenvalue problem for a special kind of acyclic matrices. Appl Math. 2019;64(3):351–366. DOI: 10.21136/AM.2019.0242-18.
  • Zarch MB, Fazeli SAS, Karbassi SM. Inverse eigenvalue problem for matrices whose graph is a banana tree. J Algor Comput. 2018;50(2):89–101.
  • Babaei Zarch M, Shahzadeh Fazeli SA. Inverse eigenvalue problem for a kind of acyclic matrices. Iranian J Sci Technol, Trans A: Sci. 2019 Jul 03;2019:1–9. DOI: 10.1007/s40995-019-00737-x. First Online.
  • Sharma D, Sen M. The minimax inverse eigenvalue problem for matrices whose graph is a generalized star of depth 2. Linear Algebra Appl. 2021;621:334–344. ISSN 0024-3795. DOI: 10.1016/j.laa.2021.03.021 .
  • Wei Y, Dai H. An inverse eigenvalue problem for the finite element model of a vibrating rod. J Comput Appl Math. 2016;300:172–182. DOI: 10.1016/j.cam.2015.12.038.
  • Nylen P, Uhlig F. Inverse eigenvalue problems associated with spring-mass systems. Linear Algebra Appl. 1997;254(1):409–425. DOI: 10.1016/S0024-3795(96)00316-3.
  • Gladwel GML. Inverse problems in vibration. Dordrecht: Kluwer Academic Publishers; 2004.
  • Li N. A matrix inverse eigenvalue problem and its application. Linear Algebra Appl. 1997;266:143–152. DOI: 10.1016/S0024-3795(96)00639-8.
  • Fiedler M. Some inverse problems for acyclic matrices. Linear Algebra Appl. 1997;253(1):113–123.
  • Horn RA, Johnson CR. Matrix analysis. New York, NY, USA: Cambridge University Press; 1986. ISBN 0-521-30586-1.
  • Hogben L. Spectral graph theory and the inverse eigenvalue problem for a graph. Electron J Linear Algebra. 2005;14:12–31. DOI: 10.13001/1081-3810.1174.