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Positive definite completions of partial Hermitian matrices
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 areExpand
Imbedding conditions for λ-matrices
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 sufficientExpand
Exposed faces and duality for symmetric and unitarily invariant norms
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 ofExpand
Czechoslovak Mathematical Journal
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 ofExpand
Faces of the unit ball of a unitarily invariant norm
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)) forExpand
Improving Hadamard's inequality *
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 thatExpand
Fibonacci numbers, alternating parity sequences and faces of the tridiagonal Birkhoff polytope
We determine the number of alternating parity sequences that are subsequences of an increasing m-tuple of integers. Expand
Multiple roots of diagonal multiples of a square matrix
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 (orExpand
Faces and traces of the unit ball of a symmetric gauge function
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 itsExpand