Skip to content
DraconiticResearch
Search Sources API
194,161 studies31 sourcesUpdated 10 min ago
PreprintarXiv licencearXiv

On properties of the conformal circulant matrices

  • Cristina Manzaneda
  • Enide Andrade
Open at sourcePDFDOICite

Abstract

In this paper, we introduce and study conformal permutation matrices. In particular, for a permutation πs∈ Sn, we define the corresponding conformal permutation matrix Hπs and show that its d−th power, where d=n/gcd(s,n), is a diagonal block matrix whose blocks are products of certain matrix blocks hi. We further show that these diagonal blocks share a common subset of eigenvalues and prove that Hπs is block-diagonalizable. We also introduce the notion of conformal circulant matrix and investigate its eigenvalues. Finally, we establish a necessary and sufficient condition for a rectangular matrix to be conformal circulant.

Related

  1. Freeness for the G-circulant Decomposition of the Partial Transpose of Random Matrices
    Octavio Arizmendi, Julian Zazueta-Obeso
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsProbabilityarXiv
  2. High-Girth QLDPC Codes from Circulant and Affine Permutation Matrices
    Vahid Nourozi, Roxana Smarandache, David G. M. Mitchell†
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Revisiting Toeplitz and Hankel random matrices via *-convergence of circulant-type matrices
    Arup Bose, Pradeep Vishwakarma
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  4. Arithmetic Conditions for the Invertibility of Circulant Matrices over Finite Fields
    Jeong-Ok Choi, Youngmi Hur
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  5. Character and Multiplier Obstructions for Circulant Weighing Matrices
    Ming Ming Tan
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{manzaneda2026properties,
  title = {{On properties of the conformal circulant matrices}},
  author = {Cristina Manzaneda and Enide Andrade},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14736},
  eprint = {2609.14736},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14736},
}
RIS
TY  - UNPB
TI  - On properties of the conformal circulant matrices
AU  - Cristina Manzaneda
AU  - Enide Andrade
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14736
UR  - https://arxiv.org/abs/2609.14736
AB  - In this paper, we introduce and study conformal permutation matrices. In particular, for a permutation π_s∈ S_n, we define the corresponding conformal permutation matrix H_π_s and show that its d−th power, where d=n/gcd(s,n), is a diagonal block matrix whose blocks are products of certain matrix blocks h_i. We further show that these diagonal blocks share a common subset of eigenvalues and prove that H_π_s is block-diagonalizable. We also introduce the notion of conformal circulant matrix and investigate its eigenvalues. Finally, we establish a necessary and sufficient condition for a rectangular matrix to be conformal circulant.
ER  -