TY - JOUR T1 - On localization of the eigenvalues of matrices "close" to triangular ones AU - Gil', Michael PY - 2022 DA - August DO - 10.15672/hujms.995747 JF - Hacettepe Journal of Mathematics and Statistics PB - Hacettepe University WT - DergiPark SN - 2651-477X SP - 1104 EP - 1107 VL - 51 IS - 4 LA - en AB - 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. KW - matrices KW - localization of eigenvalues KW - Ostrowski theorem CR - [1] A. Brauer, Limits for the characteristic roots of a matrix. II: Applications to stochastic matrices, Duke Math. J. 14 (1), 21-26, 1947. CR - [2] M. Fiedler, F.J. Hall and R. Marsli, Gershgorin discs revisited, Linear Algebra Appl. 438 (1), 598-603, 2013. CR - [3] S.A. Gershgorin. Uber die abgrenzung der eigenwerte einer matrix, Bull. Acad. des Sci. URSS 6, 749-754, 1931. CR - [4] M.I. Gil, Perturbations of determinants of matrices, Linear Algebra and its Appl. 590, 235–242, 2020. CR - [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. CR - [6] C.K. Li and F. Zhang, Eigenvalue continuity and Gershgorin’s theorem, Electron. J. Linear Algebra 35, 619-625, 2019. CR - [7] M. Marcus and H. Minc, A Survey of Matrix Theory and Matrix Inequalities, Allyn and Bacon, Boston 1964. CR - [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. CR - [9] A. Ostrowski, Uber die determinanten mit űberwiegender hauptdiagonale, Comment. Math. Helv. 10, 69-96, 1937. CR - [10] A. Ostrowski. Uber das nichtverschwinden einer klasse von determinanten und die lokalisierung der charakteristischen wurzeln von matrizen, Compositio Mathematica, 9, 209–226, 1951. UR - https://doi.org/10.15672/hujms.995747 L1 - https://dergipark.org.tr/en/download/article-file/1975512 ER -