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Publications Influence

Inverse problems for pseudo-Jacobi matrices: existence and uniqueness results

- N. Bebiano, J. Providência
- Mathematics
- 1 February 2011

This paper contains some inter-related results dealing with the general question of constructing a matrix with certain prescribed data. A theorem of Hochstadt states the unique recovery of a Jacobi… Expand

21 2

Non-Hermitian Hamiltonians with Real Spectrum in Quantum Mechanics

- J. Providência, N. Bebiano, J. Providência
- Physics
- 14 April 2011

Examples are given of non-Hermitian Hamiltonian operators which have a real spectrum. Some of the investigated operators are expressed in terms of the generators of the Weyl–Heisenberg algebra. It is… Expand

25 1

Some remarks on a conjecture of de Oliveira

- N. Bebiano, J. Providência
- Mathematics
- 1 April 1988

Abstract Let U n be the group of the unitary n × n matrices. Let A =diag(α 1 ,…,α n ), B =diag(β 1 ,…,β n ), where α 1 ,…,α n , β 1 ,…,β n are complex numbers. A class of normal matrices satisfying… Expand

12 1

Some variations on the concept of the c-numerical range

- N. Bebiano
- Mathematics
- 1986

7 1

Inverse spectral problems for structured pseudo-symmetric matrices

- N. Bebiano, J. Providência
- Mathematics
- 15 May 2013

Abstract Inverse spectral problems for Jacobi and periodic Jacobi matrices with certain sign patterns are investigated. Necessary and sufficient conditions under which the problems are solvable are… Expand

3 1

Matrix inequalities in Statistical Mechanics

- N. Bebiano, J. Providência, R. Lemos
- Mathematics
- 2004

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… Expand

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The determinant of the sum of two normal matrices with prescribed eigenvalues

- N. Bebiano, J. Queiro
- Mathematics
- 1 November 1985

Abstract Given complex numbers α 1 ,...,α n , β 1 ,...,β n , what can we say about the determinant of A + B , where A ( B ) is an n × n normal matrix with eigenvalues α 1 ,...,α n (β 1 ,...,β n )?… Expand

10 1

Indefinite numerical range of 3 × 3 matrices

- N. Bebiano, J. Providência, R. Teixeira
- Mathematics
- 11 March 2009

The point equation of the associated curve of the indefinite numerical range is derived, following Fiedler’s approach for definite inner product spaces. The classification of the associated curve is… Expand

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On the Courant–Fischer theory for Krein spaces

- N. Bebiano, H. Nakazato, J. Providência
- Mathematics
- 1 April 2009

Abstract Let J = I r ⊕ - I n - r , 0 r n . An n × n complex matrix A is said to be J-Hermitian if JA = A ∗ J . An extension of the classical theory of Courant and Fischer on the Rayleigh ratio of… Expand

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BIRKHOFF-JAMES ǫ-ORTHOGONALITY SETS IN NORMED LINEAR SPACES

The numerical range (also known as the field of values) of a square complex matrix A ∈ Cn×n is defined as F (A) = {x∗Ax ∈ C : x ∈ Cn, x∗x = 1} [8]. This range is a non-empty, compact and convex… Expand

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