Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 03 Aug 2020 21:44:24 GMT2020-08-03T21:44:24Z50291Three observations on the determinantal rangehttp://hdl.handle.net/10316/4629Title: Three observations on the determinantal range
Authors: Bebiano, N.; Soares, G.
Abstract: Let A, C [set membership, variant] Mn, the algebra of n × n complex matrices. The set of complex numbersis the C-determinantal range of A. In this note, it is proved that [Delta]C(A) is an elliptical disc for A, C [set membership, variant] M2. A necessary and sufficient condition for [Delta]C(A) to be a line segment is given when A and C are normal matrices with pairwise distinct eigenvalues. The linear operators L that satisfy the linear preserver property [Delta]C(A) = [Delta]C(L(A)), for all A, C [set membership, variant] Mn, are characterized.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10316/46292005-01-01T00:00:00ZProduct of diagonal entries of the unitary orbit of a 3-by-3 normal matrixhttp://hdl.handle.net/10316/4578Title: Product of diagonal entries of the unitary orbit of a 3-by-3 normal matrix
Authors: Nakazato, Hiroshi; Bebiano, Natália; Providência, João da
Abstract: Let N be a 3×3 normal matrix. We investigate the sets where U(3) is the group of 3×3 unitary matrices and 1[less-than-or-equals, slant]k[less-than-or-equals, slant]3. Geometric properties of these sets are studied, namely, star-shapedness and simple connectedness are investigated. A method for the numerical estimation of is also provided for normal matrices of size 3.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/45782008-01-01T00:00:00ZOn the Courant-Fischer theory for Krein spaceshttp://hdl.handle.net/10316/10045Title: On the Courant-Fischer theory for Krein spaces
Authors: Bebiano, N.; Nakazato, H.; Providência, J. da
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/100452009-01-01T00:00:00ZInequalities for quantum relative entropyhttp://hdl.handle.net/10316/4628Title: Inequalities for quantum relative entropy
Authors: Bebiano, N.; Lemos, R.; Providência, J. da
Abstract: Some logarithmic trace inequalities involving the notions of relative entropy are reobtained from a log-majorization result. The thermodynamic inequality is generalized and a chain of equivalent statements involving this inequality and the Peierls-Bogoliubov inequality is obtained.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10316/46282005-01-01T00:00:00ZInequalities for J-Hermitian matriceshttp://hdl.handle.net/10316/4624Title: Inequalities for J-Hermitian matrices
Authors: Bebiano, N.; Nakazato, H.; Providência, J. da; Lemos, R.; Soares, G.
Abstract: Indefinite versions of classical results of Schur, Ky Fan and Rayleigh-Ritz on Hermitian matrices are stated to J-Hermitian matrices, JÂ =Â IrÂ [circle plus operator]Â -InÂ -Â r, 0Â <Â rÂ <Â n). Spectral inequalities for the trace of the product of J-Hermitian matrices are presented. The inequalities are obtained in the context of the theory of numerical ranges of linear operators on indefinite inner product spaces.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10316/46242005-01-01T00:00:00ZOn the corners of certain determinantal rangeshttp://hdl.handle.net/10316/4598Title: On the corners of certain determinantal ranges
Authors: Kovačec, Alexander; Bebiano, Natália; Providência, João da
Abstract: Let A be a complex n×n matrix and let SO(n) be the group of real orthogonal matrices of determinant one. Define [Delta](A)={det(AoQ):Q[set membership, variant]SO(n)}, where o denotes the Hadamard product of matrices. For a permutation [sigma] on {1,...,n}, define It is shown that if the equation z[sigma]=det(AoQ) has in SO(n) only the obvious solutions (Q=([epsilon]i[delta][sigma]i,j), [epsilon]i=±1 such that [epsilon]1...[epsilon]n=sgn[sigma]), then the local shape of [Delta](A) in a vicinity of z[sigma] resembles a truncated cone whose opening angle equals , where [sigma]1, [sigma]2 differ from [sigma] by transpositions. This lends further credibility to the well known de Oliveira Marcus Conjecture (OMC) concerning the determinant of the sum of normal n×n matrices. We deduce the mentioned fact from a general result concerning multivariate power series and also use some elementary algebraic topology.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10316/45982007-01-01T00:00:00ZMatrix inequalities in Statistical Mechanicshttp://hdl.handle.net/10316/11431Title: Matrix inequalities in Statistical Mechanics
Authors: Bebiano, N.; Providência Jr., J. da; Lemos, R.
Abstract: Some matrix inequalities used in statistical mechanics are presented. A
straightforward proof of the Thermodynamic Inequality is given and its equivalence
to the Peierls–Bogoliubov inequality is shown.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10316/114312003-01-01T00:00:00ZOn the geometry of numerical ranges in spaces with an indefinite inner producthttp://hdl.handle.net/10316/4632Title: On the geometry of numerical ranges in spaces with an indefinite inner product
Authors: Bebiano, N.; Lemos, R.; Providência, J. da; Soares, G.
Abstract: Geometric properties of the numerical ranges of operators on an indefinite inner product space are investigated. In particular, classes of matrices are presented such that the boundary generating curves of the J-numerical range are hyperbolical. The curvature of the J-numerical range at a boundary point is studied, generalizing results of Fiedler on the classical numerical range.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10316/46322005-01-01T00:00:00ZThe J-numerical range of a J-Hermitian matrix and related inequalitieshttp://hdl.handle.net/10316/4585Title: The J-numerical range of a J-Hermitian matrix and related inequalities
Authors: Nakazato, Hiroshi; Bebiano, Natália; Providência, João da
Abstract: Recently, indefinite versions of classical inequalities of Schur, Ky Fan and Rayleigh-Ritz on Hermitian matrices have been obtained for J-Hermitian matrices that are J-unitarily diagonalizable, J=Ir[circle plus operator](-Is),r,s>0. The inequalities were obtained in the context of the theory of numerical ranges of operators on indefinite inner product spaces. In this paper, the subject is revisited, relaxing the constraint of the matrices being J-unitarily diagonalizable.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/45852008-01-01T00:00:00ZThe numerical range of 2-dimensional Krein spaces operatorshttp://hdl.handle.net/10316/11374Title: The numerical range of 2-dimensional Krein spaces operators
Authors: Nakazato, Hiroshi; Bebiano, Natália; Providência, João da
Abstract: The tracial numerical range of operators on a 2-dimensional Krein
space is investigated. Results in the vein of those obtained in the context of Hilbert
spaces are stated
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10316/113742006-01-01T00:00:00ZGeometry of the numerical range of Krein space operatorshttp://hdl.handle.net/10316/11306Title: Geometry of the numerical range of Krein space operators
Authors: Bebiano, N.; Providência, J. da; Teixeira, R.
Abstract: The characteristic polynomial of the pencil generated by two J-Hermitian
matrices is studied in connection with the numerical range. Geometric properties
of the numerical range of linear operators on an inde nite inner product space
are investigated. The point equation of the associated curve of the numerical range
is derived, following Fiedler's approach for de nite inner product spaces. The classi
cation of the associated curve in the 3 £ 3 case is presented, using Newton's
classi cation of cubic curves. As a consequence, the respective numerical ranges are
characterized. Illustrative examples of all the di erent possibilities are given.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10316/113062007-01-01T00:00:00ZA fiedler-type theorem for the determinant of J-positive matriceshttp://hdl.handle.net/10316/44384Title: A fiedler-type theorem for the determinant of J-positive matrices
Authors: Bebiano, Natália; da Providência, João
Fri, 01 Apr 2016 00:00:00 GMThttp://hdl.handle.net/10316/443842016-04-01T00:00:00ZAn algorithm for constructing a pseudo-Jacobi matrix from given spectral datahttp://hdl.handle.net/10316/44377Title: An algorithm for constructing a pseudo-Jacobi matrix from given spectral data
Authors: Bebiano, Natália; Furtado, Susana; da Providência, João
Fri, 01 Mar 2013 00:00:00 GMThttp://hdl.handle.net/10316/443772013-03-01T00:00:00ZThe numerical range of banded biperiodic Toeplitz operatorshttp://hdl.handle.net/10316/44344Title: The numerical range of banded biperiodic Toeplitz operators
Authors: Bebiano, Natália; da Providência, João; Nata, Ana
Fri, 01 Feb 2013 00:00:00 GMThttp://hdl.handle.net/10316/443442013-02-01T00:00:00ZImplications of losing Hermiticity in quantum mechanicshttp://hdl.handle.net/10316/44380Title: Implications of losing Hermiticity in quantum mechanics
Authors: Bebiano, Natália; da Providência, João
Mon, 12 Sep 2016 00:00:00 GMThttp://hdl.handle.net/10316/443802016-09-12T00:00:00ZFields of values of linear pencils and spectral inclusion regionshttp://hdl.handle.net/10316/44402Title: Fields of values of linear pencils and spectral inclusion regions
Authors: Bebiano, Natália; da Providência, João; Nata, Ana; da Providência, J. P.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10316/444022017-01-01T00:00:00ZAn inverse indefinite numerical range problemhttp://hdl.handle.net/10316/44379Title: An inverse indefinite numerical range problem
Authors: Bebiano, Natália; da Providência, João; Nata, Ana; da Providência, J. P.
Wed, 01 Apr 2015 00:00:00 GMThttp://hdl.handle.net/10316/443792015-04-01T00:00:00ZThe EMM and the spectral analysis of a non self-adjoint Hamiltonian on an infinite dimensional Hilbert spacehttp://hdl.handle.net/10316/44378Title: The EMM and the spectral analysis of a non self-adjoint Hamiltonian on an infinite dimensional Hilbert space
Authors: Bebiano, Natália; da Providência, João
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10316/443782016-01-01T00:00:00ZComputing the numerical range of Krein space operatorshttp://hdl.handle.net/10316/44403Title: Computing the numerical range of Krein space operators
Authors: Bebiano, Natália; da Providência, João; Nata, Ana; da Providência, J. P.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10316/444032015-01-01T00:00:00ZThe characteristic polynomial of linear pencils of small size and the numerical rangehttp://hdl.handle.net/10316/44382Title: The characteristic polynomial of linear pencils of small size and the numerical range
Authors: Bebiano, Natália; da Providência, João; Esmaeili, F.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10316/443822017-01-01T00:00:00ZDeterminantal inequalities for J-accretive dissipative matriceshttp://hdl.handle.net/10316/44385Title: Determinantal inequalities for J-accretive dissipative matrices
Authors: Bebiano, Natália; da Providência, João
Abstract: In this note we determine bounds for the determinant of the sum of two J-accretive dissipative matrices with prescribed spectra.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10316/443852017-01-01T00:00:00ZRevisiting the inverse field of values problemahttp://hdl.handle.net/10316/44404Title: Revisiting the inverse field of values problema
Authors: Bebiano, Natália; da Providência, João; Nata, Ana; da Providência, J. P.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/444042014-01-01T00:00:00ZOn generalized numerical ranges of operators on an indefinite inner product spacehttp://hdl.handle.net/10316/11439Title: On generalized numerical ranges of operators on an indefinite inner product space
Authors: Bebiano, N.; Lemos, R.; Providência, J. da; Soares, G.
Abstract: In this paper, numerical ranges associated to operators on an inde nite
inner product space are investigated. Boundary generating curves, corners, shapes
and computer generations of these sets are studied. In particular, the Murnaghan-
Kippenhahn theorem for the classical numerical range is generalized.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10316/114392003-01-01T00:00:00ZConvexity of the Krein space tracial numerical range and Morse theoryhttp://hdl.handle.net/10316/13648Title: Convexity of the Krein space tracial numerical range and Morse theory
Authors: Nakazato, Hiroshi; Bebiano, Natália; Providência, João da
Abstract: In this paper we present a Krein space convexity theorem on the tracial-numerical range of a matrix. This theorem is the analogue of Westwick's theorem.
The proof is an application of Morse theory.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/136482009-01-01T00:00:00ZFlat portions on the boundary of the indefinite numerical range of 3×3 matriceshttp://hdl.handle.net/10316/4584Title: Flat portions on the boundary of the indefinite numerical range of 3×3 matrices
Authors: Bebiano, N.; Providência, J. da; Teixeira, R.
Abstract: We focus on complex 3×3 matrices whose indefinite numerical ranges have a flat portion on the boundary. The results here obtained are parallel to those of Keeler, Rodman and Spitkovsky for the classical numerical range.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/45842008-01-01T00:00:00ZThe boundary of the Krein space tracial numerical range, an algebraic approach and a numerical algorithmhttp://hdl.handle.net/10316/13644Title: The boundary of the Krein space tracial numerical range, an algebraic approach and a numerical algorithm
Authors: Bebiano, N.; Nakazato, H.; Nata, A.; Providência, J. da
Abstract: In this article, tracial numerical ranges associated with matrices in an
inde nite inner product space are investigated. The boundary equations of these
sets are obtained and the case of the boundary being a polygon is studied. As
an application, a numerical algorithm for plotting the tracial numerical range of
an arbitrary complex matrix, is presented. Our approach uses the elementary idea
that the boundary may be traced by computing the supporting lines.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/136442009-01-01T00:00:00ZClasses of non-Hermitian operators with real eigenvalueshttp://hdl.handle.net/10316/13628Title: Classes of non-Hermitian operators with real eigenvalues
Authors: Bebiano, Natália; Providência, J. da; Providência, João P. da
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/136282009-01-01T00:00:00ZProducts of Laurent operators and fields of valueshttp://hdl.handle.net/10316/44386Title: Products of Laurent operators and fields of values
Authors: Bebiano, Natália; da Providência, João
Tue, 01 Nov 2016 00:00:00 GMThttp://hdl.handle.net/10316/443862016-11-01T00:00:00ZNumerical ranges of unbounded operators arising in quantum physicshttp://hdl.handle.net/10316/4639Title: Numerical ranges of unbounded operators arising in quantum physics
Authors: Bebiano, N.; Lemos, R.; Providência, J. da
Abstract: Creation and annihilation operators are used in quantum physics as the building blocks of linear operators acting on Hilbert spaces of many body systems. In quantum physics, pairing operators are defined in terms of those operators. In this paper, spectral properties of pairing operators are studied. The numerical ranges of pairing operators are investigated. In the context of matrix theory, the results give the numerical ranges of certain infinite tridiagonal matrices.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10316/46392004-01-01T00:00:00Z