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Circulant matrices with orthogonal rows and off-diagonal entries of absolute value 1

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F21%3AA22029W9" target="_blank" >RIV/61988987:17310/21:A22029W9 - isvavai.cz</a>

  • Alternative codes found

    RIV/61389005:_____/21:00544707

  • Result on the web

    <a href="https://sciendo.com/article/10.2478/cm-2021-0005" target="_blank" >https://sciendo.com/article/10.2478/cm-2021-0005</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.2478/cm-2021-0005" target="_blank" >10.2478/cm-2021-0005</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Circulant matrices with orthogonal rows and off-diagonal entries of absolute value 1

  • Original language description

    It is known that a real symmetric circulant matrix with diagonal entries d ≥ 0, off-diagonal entries ±1 and orthogonal rows exists only of order 2d + 2 (and trivially of order 1) [Turek and Goyeneche 2019]. In this paper we consider a complex Hermitian analogy of those matrices. That is, we study the existence and construction of Hermitian circulant matrices having orthogonal rows, diagonal entries d ≥ 0 and any complex entries of absolute value 1 off the diagonal. As a particular case, we consider matrices whose off-diagonal entries are 4th roots of unity; we prove that the order of any such matrix with d different from an odd integer is n = 2d + 2. We also discuss a similar problem for symmetric circulant matrices defined over finite rings Zm. As an application of our results, we show a close connection to mutually unbiased bases, an important open problem in quantum information theory.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2021

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Communications in Mathematics

  • ISSN

    1804-1388

  • e-ISSN

    2336-1298

  • Volume of the periodical

    29

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    CZ - CZECH REPUBLIC

  • Number of pages

    20

  • Pages from-to

    15-34

  • UT code for WoS article

  • EID of the result in the Scopus database

    2-s2.0-85105719712