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Positive definite completions of partial Hermitian matrices

- R. Grone, C. Johnson, E. M. Sá, H. Wolkowicz
- Mathematics
- 1 April 1984

Abstract The question of which partial Hermitian matrices (some entries specified, some free) may be completed to positive definite matrices is addressed. It is shown that if the diagonal entries are… Expand

521 31- PDF

Imbedding conditions for λ-matrices

- E. M. Sá
- Mathematics
- 1 April 1979

Abstract We say that A (λ) is λ-imbeddable in B (λ) whenever B (λ) is equivalent to a λ-matrix having A (λ) as a submatrix. In this paper we solve the problem of finding a necessary and sufficient… Expand

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Exposed faces and duality for symmetric and unitarily invariant norms

- E. M. Sá
- Mathematics
- 1994

Abstract Let ψ be a unitarily invariant norm on the space of (real or complex) n×m matrices, and g the associated symmetric gauge function: thus ψ(A)g(s(A)), where s(A) is the decreasing sequence of… Expand

22 2- PDF

Czechoslovak Mathematical Journal

- E. M. Sá
- 2016

Czechoslovak Mathematical Journal publishes original research papers of high scientific quality in mathematics. The journal is published quarterly in issues containing 288 pages each. Manuscripts of… Expand

20 2- PDF

Faces of the unit ball of a unitarily invariant norm

- E. M. Sá
- Mathematics
- 1994

Abstract Let ψ be a unitarily invariant norm on the space of all n×m complex matrices, and let g: R n→ R be the symmetric gauge function associated with ψ. That is to say, we have ψ(A)g(s(A)) for… Expand

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Improving Hadamard's inequality *

- B. Grone, C. Johnson, E. M. Sá, H. Wolkowicz
- Mathematics
- 1 December 1984

We study several bounds for the determinant of an n × n positive definite Hermitian matrix A. These bounds are the best possible given certain data about A. We find the best bounds in the cases that… Expand

14- PDF

Fibonacci numbers, alternating parity sequences and faces of the tridiagonal Birkhoff polytope

- C. Fonseca, E. M. Sá
- Computer Science, Mathematics
- Discret. Math.
- 1 April 2008

TLDR

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Multiple roots of diagonal multiples of a square matrix

- E. M. Sá
- Mathematics
- 1981

We find conditions on an n-square matrix A, over a field F of characteristic +2, that are equivalent 10 the following property: for any n-diagonal Dover F, the matrix DA has a multiple eigenvalue (or… Expand

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Faces and traces of the unit ball of a symmetric gauge function

- E. M. Sá
- Mathematics
- 1994

Abstract We investigate the faces of the closed unit ball, Bg≔{x:g(x)⩽1}, of a symmetric gauge function g: R n→ R +. Firstly, we describe the group of symmetries of a face F of Bg, in terms of its… Expand

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