G. Soares
University of Trás-os-Montes and Alto Douro
Network
Latest external collaboration on country level. Dive into details by clicking on the dots.
Publication
Featured researches published by G. Soares.
Linear & Multilinear Algebra | 2004
Natália Bebiano; R. Lemos; J. da Providência; G. Soares
In this article, numerical ranges associated with operators on an indefinite 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.
Linear & Multilinear Algebra | 2001
Chi-Kwong Li; Peter Šemrl; G. Soares
We characterize those linear operators on triangular or diagonal matrices preserving the numerical range or radius.
Linear & Multilinear Algebra | 2013
Alexander E. Guterman; R. Lemos; G. Soares
For A, C ∈ M n the C-determinantal range of A is the following set on the complex plane ▵ C (A) = {det(A − UCU*): UU* = I n }. For normal matrices A and C with eigenvalues α1, … , α n and γ1, … , γ n , respectively, Marcus [M. Marcus, Derivations, Plücker relations and the numerical range, Indiana Univ. Math. J. 22 (1973), pp. 1137–1149] and Oliveira [G.N. de Oliveira, Normal matrices (research problem), Linear Multilinear Algebra 12 (1982), pp. 153–154] conjectured that ▵ C (A) is a subset of the convex hull of the points , σ ∈ S n , where S n is the symmetric group of degree n. We investigate the extremal set of matrices for which the equality holds in the Marcus–Oliveira conjecture. We illustrate the use of the obtained results by two different applications. The first one deals with the equality case between the radius of ▵ C (A) and the radius of the convex hull of the points z σ, σ ∈ S n . The second one is the characterization of additive Frobenius endomorphisms for the determinantal range or radius on the space M n and on its real subspace of Hermitian matrices.
Applied Mathematics and Computation | 2016
Alexander E. Guterman; R. Lemos; G. Soares
Let A and C be square complex matrices of size n, the C-determinantal range of A is the subset of the complex plane { det ( A - U C U * ) : U U * = I n } . If A, C are both Hermitian matrices, then by a result of Fiedler (1971) 11 this set is a real line segment.In our paper we study this set for the case when C is a Hermitian matrix. Our purpose is to revisit and improve two well-known results on this topic. The first result is due to Li concerning the C-numerical range of a Hermitian matrix, see Condition 5.1?(a) in Li, (1994) 20. The second one is due to C.-K. Li, Y.-T. Poon and N.-S. Sze about necessary and sufficient conditions for the C-determinantal range of A to be a subset of the line, (see Li et?al. (2008) 21, Theorem 3.3).
Linear Algebra and its Applications | 2005
Natália Bebiano; R. Lemos; J. da Providência; G. Soares
Linear Algebra and its Applications | 2005
Natália Bebiano; Hiroshi Nakazato; J. da Providência; R. Lemos; G. Soares
Mathematical Inequalities & Applications | 2010
Natália Bebiano; R. Lemos; João da Providência; G. Soares
Mathematical Inequalities & Applications | 2012
Natália Bebiano; R. Lemos; João da Providência; G. Soares
The Journal of Advanced Research in Applied Mathematics | 2009
Natália Bebiano; R. Lemos; J. da Providência; G. Soares
Archive | 2009
G. Soares