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Resolvent comparison for Hermitian block matrices and Kelmans transformations — arXiv:2611.04688

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.04688
License (as archived): CC0-1.0
Archived: 2026-11-04T19:01:39.743Z
SHA-256 of the archived text: d2d99252059f89f54548dceb7f1f2e714c8954a1d5307d5e1a5f5a9220a645bc
Stable URL of this page: https://metraipolis.com/documento/dc_bb259ba75681

How to cite

Resolvent comparison for Hermitian block matrices and Kelmans transformations — arXiv:2611.04688 — arXiv (en), https://arxiv.org/abs/2611.04688 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bb259ba75681 (Metraipolis archive dc_bb259ba75681, sha256 d2d99252059f89f54548dceb7f1f2e714c8954a1d5307d5e1a5f5a9220a645bc)

BibTeX

@misc{dcbb259ba75681,
  title = {Resolvent comparison for Hermitian block matrices and Kelmans transformations — arXiv:2611.04688},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.04688},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bb259ba75681; sha256 d2d99252059f89f54548dceb7f1f2e714c8954a1d5307d5e1a5f5a9220a645bc},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.04688. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A Kelmans transformation increases or preserves the largest eigenvalue of a symmetric nonnegative matrix. We determine when this comparison holds for Hermitian block extensions with a fixed coupling and an arbitrary common complementary block. An orthogonal change of basis and Schur complementation give an exact formula for the compressed resolvent difference as a difference of two rank-one matrices. This formula characterizes admissible coupling subspaces by proportionality of projected resolvent vectors. Polynomial coefficient kernels describe all such subspaces, and cyclic subspaces give dimension bounds and a maximum-dimension result for a two-block family. We also prove a general block comparison theorem and give monotonicity and equality criteria for nonnegative rank-one couplings. Applications concern graph joins, complex attachments, and Hermitian adjacency matrices.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Rings and Algebras (math.RA) ; Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2611.04688 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-04T18:38:22.340Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).