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Inverse problems for pseudo-Jacobi matrices: existence and uniqueness results
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 JacobiExpand
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Non-Hermitian Hamiltonians with Real Spectrum in Quantum Mechanics
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 isExpand
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Some remarks on a conjecture of de Oliveira
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 satisfyingExpand
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Inverse spectral problems for structured pseudo-symmetric matrices
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 areExpand
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Matrix inequalities in Statistical Mechanics
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 isExpand
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The determinant of the sum of two normal matrices with prescribed eigenvalues
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
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Indefinite numerical range of 3 × 3 matrices
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 isExpand
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On the Courant–Fischer theory for Krein spaces
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 ofExpand
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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 convexExpand
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