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Fundam. Prikl. Mat., 2007, Volume 13, Issue 4, Pages 67–94 (Mi fpm1064)  

This article is cited in 9 scientific papers (total in 9 papers)

Cramer's rule for quaternionic systems of linear equations

I. I. Kirchei

Ya. S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NAS Ukraine

Abstract: New definitions of determinant functionals over the quaternion skew field are given in this paper. The inverse matrix over the quaternion skew field is represented by analogues of the classical adjoint matrix. Cramer's rules for right and left quaternionic systems of linear equations have been obtained.

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English version:
Journal of Mathematical Sciences (New York), 2008, 155:6, 839–858

Bibliographic databases:

UDC: 512.643.2

Citation: I. I. Kirchei, “Cramer's rule for quaternionic systems of linear equations”, Fundam. Prikl. Mat., 13:4 (2007), 67–94; J. Math. Sci., 155:6 (2008), 839–858

Citation in format AMSBIB
\Bibitem{Kir07}
\by I.~I.~Kirchei
\paper Cramer's rule for quaternionic systems of linear equations
\jour Fundam. Prikl. Mat.
\yr 2007
\vol 13
\issue 4
\pages 67--94
\mathnet{http://mi.mathnet.ru/fpm1064}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2366237}
\zmath{https://zbmath.org/?q=an:1157.15308}
\elib{http://elibrary.ru/item.asp?id=11162675}
\transl
\jour J. Math. Sci.
\yr 2008
\vol 155
\issue 6
\pages 839--858
\crossref{https://doi.org/10.1007/s10958-008-9245-6}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-57349192046}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. B. Poplavskii, “Formuly Kramera dlya sistem lineinykh uravnenii i neravenstv nad bulevoi algebroi”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 11:3(2) (2011), 43–46  mathnet
    2. Poplavskii V.B., “Ob opredelitelyakh matrits nad polyami, koltsami i polukoltsami”, Vestnik Moskovskoi gosudarstvennoi akademii delovogo administrirovaniya. Seriya: Filosofskie, sotsialnye i estestvennye nauki, 2011, no. 5, 158–165  mathscinet  elib
    3. A. M. Galmak, “Vektor-opredeliteli i opredeliteli vektor-matrits”, PFMT, 2011, no. 2(7), 58–64  mathnet
    4. Kyrchei I., “Weighted Singular Value Decomposition and Determinantal Representations of the Quaternion Weighted Moore-Penrose Inverse”, Appl. Math. Comput., 309 (2017), 1–16  crossref  mathscinet  isi  scopus
    5. Kyrchei I., “Cramer'S Rules For Some Hermitian Coquaternionic Matrix Equations”, Adv. Appl. Clifford Algebr., 27:3, SI (2017), 2509–2529  crossref  mathscinet  zmath  isi  scopus
    6. Kyrchei I., “Cramer'S Rules For Sylvester Quaternion Matrix Equation and Its Special Cases”, Adv. Appl. Clifford Algebr., 28:5 (2018), UNSP 90  crossref  mathscinet  isi  scopus
    7. Song G.-J., Wang Q.-W., Yu Sh.-W., “Cramer'S Rule For a System of Quaternion Matrix Equations With Applications”, Appl. Math. Comput., 336 (2018), 490–499  crossref  mathscinet  isi  scopus
    8. Kyrchei I.I., “Explicit Determinantal Representation Formulas For the Solution of the Two-Sided Restricted Quaternionic Matrix Equation”, J. Appl. Math. Comput., 58:1-2 (2018), 335–365  crossref  mathscinet  zmath  isi  scopus
    9. Kyrchei I., “Determinantal Representations of Solutions to Systems of Quaternion Matrix Equations”, Adv. Appl. Clifford Algebr., 28:1 (2018), UNSP 23  crossref  mathscinet  isi  scopus
  • Фундаментальная и прикладная математика
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