Self-adjoint block operator matrices with non-separated diagonal entries and their Schur complements
نویسندگان
چکیده
منابع مشابه
Special H-matrices and their Schur and diagonal-Schur complements
It is well known, see [D. Carlson, T. Markham, Schur complements of diagonally dominant matrices, Czech. Math. Schur complement of a strictly diagonally dominant matrix is strictly diagonally dominant , as well as its diagonal-Schur complement. Also, if a matrix is an H-matrix, then its Schur complement and diagonal-Schur complement are H-matrices, too, see [J. Liu, Y. Huang, Some properties on...
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The definitions of θ-ray pattern matrix and θ-ray matrix are firstly proposed to establish some new results on nonsingularity/singularity and convergence of general H-matrices. Then some conditions on the matrix A ∈ Cn×n and nonempty α ⊂ 〈n〉 = {1, 2, . . . , n} are proposed such that A is an invertible H-matrix if A(α) and A/α are both invertible H-matrices. Furthermore, the important results o...
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We study the spectrum of unbounded J-self-adjoint block operator matrices. In particular, we prove enclosures for the spectrum, provide a sufficient condition for the spectrum being real and derive variational principles for certain real eigenvalues even in the presence of non-real spectrum. The latter lead to lower and upper bounds and asymptotic estimates for eigenvalues. AMS Subject classifi...
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The Schur-Horn Theorem states that there exists a self-adjoint matrix with a given spectrum and diagonal if and only if the spectrum majorizes the diagonal. Though the original proof of this result was nonconstructive, several constructive proofs have subsequently been found. Most of these constructive proofs rely on Givens rotations, and none have been shown to be able to produce every example...
متن کاملFurther results on H-matrices and their Schur complements
It is well-known [D. Carlson, T. Markham, Schur complements of diagonally dominant matrices, Czech. Math. J. 29 (104) (1979) 246–251, [1]] that the Schur complement of a strictly diagonally dominant matrix is strictly diagonally dominant. Also, if a matrix is an H-matrix, then its Schur complement is an H-matrix, too [J. Liu, Y. Huang, Some properties on Schur complements of H-matrices and diag...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2003
ISSN: 0022-1236
DOI: 10.1016/s0022-1236(02)00115-5