Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 15 Aug 2020 17:50:56 GMT2020-08-15T17:50:56Z5031Inverse eigenvalue problems and lists of multiplicities of eigenvalues for matrices whose graph is a tree: the case of generalized stars and double generalized starshttp://hdl.handle.net/10316/11451Title: Inverse eigenvalue problems and lists of multiplicities of eigenvalues for matrices whose graph is a tree: the case of generalized stars and double generalized stars
Authors: Johnson, Charles R.; Duarte, António Leal; Saiago, Carlos M.
Abstract: We characterize the possible lists of ordered multiplicities among
matrices whose graph is a generalized star (a tree in which at most
one vertex has degree greater than 2) or a double generalized star.
Here, the inverse eigenvalue problem for symmetric matrices whose
graph is a generalized star is settled. The answer is consistent with a
conjecture that determination of the possible ordered multiplicities is
equivalent to the inverse eigenvalue problem for a given tree. Moreover,
a key spectral feature of the inverse eigenvalue problem in the
case of generalized stars is shown to characterize them among trees.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10316/114512002-01-01T00:00:00ZThe change in eigenvalue multiplicity associated with perturbation of a diagonal entry of the matrixhttp://hdl.handle.net/10316/13630Title: The change in eigenvalue multiplicity associated with perturbation of a diagonal entry of the matrix
Authors: Johnson, Charles R.; Duarte, António Leal; Saiago, Carlos M.
Abstract: Here we investigate the relation between perturbing the i-th diagonal
entry of A 2 Mn(F) and extracting the principal submatrix A(i) from A with
respect to the possible changes in multiplicity of a given eigenvalue. A complete
description is given and used to both generalize and improve prior work about
Hermitian matrices whose graph is a given tree.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/136302009-01-01T00:00:00ZThe structure of matrices with a maximum multiplicity eigenvaluehttp://hdl.handle.net/10316/4579Title: The structure of matrices with a maximum multiplicity eigenvalue
Authors: Johnson, Charles R.; Duarte, António Leal; Saiago, Carlos M.
Abstract: There is remarkable and distinctive structure among Hermitian matrices, whose graph is a given tree T and that have an eigenvalue of multiplicity that is a maximum for T. Among such structure, we give several new results: (1) no vertex of T may be "neutral"; (2) neutral vertices may occur if the largest multiplicity is less than the maximum; (3) every Parter vertex has at least two downer branches; (4) removal of a Parter vertex changes the status of no other vertex; and (5) every set of Parter vertices forms a Parter set. Statements (3), (4) and (5) are also not generally true when the multiplicity is less than the maximum. Some of our results are used to give further insights into prior results, and both the review of necessary background and the development of new structural lemmas may be of independent interest.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/45792008-01-01T00:00:00Z