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
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Czech description
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Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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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
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EID of the result in the Scopus database
2-s2.0-85105719712