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Biography
Dr. Ivan Kyrchei

Dr. Ivan Kyrchei

Department of differential equations and theory of functions

Pidstryhach Institute for Applied Problems of Mechanics and Mathematics,

NAS of Ukraine, Ukraine

Senior Researcher


Email: kyrchei@online.ua


Qualifications

2008 Ph.D., Taras Shevchenko National University of Kyiv, Ukraine

1982 M.S., Ivan Franko National University of Lviv, Ukraine


Publications (Selected)

Books, Book Chapters

  1. KYRCHEI, Ivan: Cramer's Rule for Generalized Inverse Solutions. In: KYRCHEI, Ivan (Ed.): Advances in Linear Algebra Research. New York: Nova Sci. Publ., 2015, pp. 79-132.–ISBN 978-1-63463-565-3
  2. KLEYN,Aleks; KYRCHEI, Ivan:Relation of Row-Column Determinants with Quasideter- minants of Matrices over a Quaternion Algebra. In: KYRCHEI, Ivan (Ed.): Advances in Linear Algebra Research. New York: Nova Sci. Publ., 2015, pp.299-324.–ISBN 978-1-63463-565-3
  3. KYRCHEI, Ivan: The Theory of The Column And Row Determinants in a Quaternion Linear Algebra. In: Albert R. Baswell (Ed.): Advances in Mathematics Research 15. New York: Nova Sci. Publ., 2012, pp. 301-359.–ISBN 978-1-62417-511-4
  4. KYRCHEI, Ivan: Determinantal Representations of the Drazin and W-Weighted Drazin Inverses Over the Quaternion Skew Field with Applications., In: Sandra Griffin (Ed.): Quaternions: Theory and Applications. New York: Nova Sci. Publ., 2017, pp.201-275
  5. KYRCHEI, Ivan: Determinantal Representations of the Quaternion Weighted Moore-Penrose Inverse and Its Applications, In: Albert R. Baswell (Ed.): Advances in Mathematics Research 23. New York: Nova Sci. Publ., 2017, pp. 35-96. –ISBN 978-1-53612-512-2


Scientific Journals

  1. KYRCHEI, Ivan, 2017. Explicit determinantal representation formulas for the solution of the two-sided restricted quaternionic matrix equation, Journal of Applied Mathematics and Computing. Available from:https://doi.org/10.1007/s12190-017-1148-6
  2. KYRCHEI, Ivan, 2017. Weighted singular value decomposition and determinantal representations of the quaternion weighted Moore–Penrose inverse, Applied Mathematics and Computation, vol. 309, pp. 1-16. ISSN 0096-3003. Available from: https://doi.org/10.1016/j.amc.2017.03.048
  3. KYRCHEI, Ivan, 2017. The column and row immanants of matrices over a split quaternion algebra. Advances in Applied Clifford Algebras, vol. 27(3), pp. 2509–2529. ISSN 1661-4909. Available from: https://doi.org/10.1007/s00006-016-0751-1
  4. Hajarian, Masoud; Yuan, Jinyun; Kyrchei, Ivan, 2016. Applications of methods of numerical linear algebra in engineering 2016, Mathematical Problems in Engineering, 2016) Vol. 2016, Article ID 4854759, 2 pages. Available from: https://dx.doi.org/10.1155/2016/4854759
  5. KYRCHEI, Ivan, 2016. Explicit determinantal representation formulas of W-weighted Drazin inverse solutions of some matrix equations over the quaternion skew field, Mathematical Problems in Engineering, (2016) Vol. 2016, Article ID 8673809, 13 pages. Available from: http://dx.doi.org/10.1155/2016/8673809
  6. KYRCHEI, Ivan, 2015. Determinantal representations of the W-weighted Drazin inverse over the quaternion skew field. Applied Mathematics and Computation, vol. 264 (1), pp. 453-465. ISSN 0096-3003. Available from: http://www.sciencedirect.com/science/article/pii/S0096300315005962
  7. KYRCHEI, Ivan, 2015. The column and row immanants of matrices over a split quaternion algebra. Advances in Applied Clifford Algebras, in press. ISSN 0188-7009. Available from: http://link.springer.com/article/10.1007/s00006-014-0517-6
  8. KYRCHEI, Ivan, 2014. Determinantal Representations of the Drazin Inverse over the Quaternion Skew Field with Applications to Some Matrix Equations.Applied Mathematics and Computation,vol.238, pp. 193–207.ISSN0096-3003
  9. KYRCHEI, Ivan, 2013.Explicit Formulas for Determinantal Representations of the Drazin Inverse Solutions of Some Matrix and Differential Matrix Equations.Applied Mathematics and Computation,vol.219, pp. 7632-7644.ISSN0096-3003
  10. KYRCHEI, Ivan, 2013. Explicit Representation Formulas for the Minimum Norm Least Squares Solutions of Some Quaternion Matrix Equations.Linear Algebra Appl.,vol. 438, no. 1, pp. 136-152.ISSN0024-3795
  11. KYRCHEI, Ivan, 2012. Analogs of Cramer'S Rule for the Minimum Norm Least Squares Solutions of Some Matrix Equations.Applied Mathematics and Computation,vol.218, pp.6375-6384.ISSN0096-3003
  12. KYRCHEI, Ivan, 2012. Determinantal Representation of The Moore-Penrose Inverse Matrix over the Quaternion Skew Field.Journal of Mathematical Sciences,vol.180, no.1, pp 23-33.ISSN1072-3374
  13. KYRCHEI, Ivan, 2011. Determinantal Representations of the Moore-Penrose Inverse over the Quaternion Skew Field and Corresponding Cramer'S Rules.Linear Multilinear Algebra,vol.59, no.4, pp. 413-431.ISSN0308-1087
  14. KYRCHEI, Ivan, 2010.Cramer'S Rule for Some Quaternion Matrix Equations.Applied Mathematics and Computation,vol.217, no.5, pp. 2024-2030.ISSN0096-3003
  15. KYRCHEI, Ivan, 2008.Analogs of the Adjoint Matrix for Generalized Inverses and Corresponding Cramer Rules,Linear and Multilinear Algebra,vol.56, no.4, pp. 453-469.ISSN0308-1087
  16. KYRCHEI, Ivan, 2008. Cramer'S Rule for Quaternionic Systems of Linear Equations,Journal of Mathematical Sciences,vol.155, no.6, pp 839-858.ISSN1072-3374
  17. KYRCHEI, Ivan, 2006. Cramer Rule Over Quaternion Division Algebra.Bulletin of the University of Kiev. Series: Physics and Mathematics, no. 1, pp.28-34.ISSN28-341728-3817
  18. KYRCHEI, Ivan, 2006. Determinantal Representation of the Drazin.Mathematical Methods and Physicomechanical Fields,vol.49, no.2, pp.58–64.ISSN0130–9420
  19. KYRCHEI, Ivan, 2004.Representation of Generalized Inverse Moore–Penrose Matrix by Analog of Classical Adjoint Matrix.Mathematical Methods and Physicomechanical Fields,vol.47, no.4, pp.6–11.ISSN0130–9420
  20. KYRCHEI, Ivan, 2003. Analogue of Adjoint Matrix over Skew Field with Involution.Mathematical Methods and Physicomechanical Fields,vol.46, no.4, pp.81-91.ISSN0130–9420
  21. KYRCHEI, Ivan, 2002. The Inverse Matrix for Hermitian over a Quasi-Field.Visnyk Lviv Univ. Ser. Appl. Math. Comp. Sci.No 4. pp. 120-125.ISSN2078-5097
  22. KYRCHEI, Ivan, 2001. Classical Adjoint for Hermitian Matrix over Quasi-Field.Mathema- tical Methods and Physicomechanical Fields,vol.44, no.3, pp.33–49.ISSN0130–9420
  23. KYRCHEI, Ivan, 1998. Fractional-Rational Regularization of a System of Linear Equations over the Skew-Field of Quaternions.Journal of Mathematical Sciences,vol.90, no.5, pp 2398-2403.ISSN1072-3374


International Conference Papers

  1. KYRCHEI, Ivan: Cramer's Rule for Two-sided Restricted Quaternionic Matrix Equation. In: Book of abstracts of Conference: 11th International Algebraic Conference in Ukraine dedicated to the 75th anniversary of V. V. Kirichenko, At Kyiv, Ukraine
  2. KYRCHEI, Ivan: Determinantal representations of the weighted Moore-Penrose inverse matrix over the quaternion skew field. In: Book of abstracts of Conference: Algebra and Logic: Theory and Applications International Conference dedicated to the 70th anniversary of V. M. Levchuk, At Krasnoyarsk. Russia
  3. KYRCHEI, Ivan: Determinantal representation of the W-weighted Drazin inverse over the quaternion skew field. In: Book of abstracts of X International Algebraic Conference in Ukraine dedicated to the 70th anniversary of Yu. A. Drozd, (Odessa, August 20-27, 2015)
  4. KYRCHEI, Ivan: Preface of the "Minisymposium on Theory and Application of Matrix Equations".In: AIP Conference Proceedings of ICNAAM 2014 (Rhodes, 22–28 September 2014), vol. 1648, p.340001. - ISBN 978-0-7354-1287-3
  5. KYRCHEI, Ivan: Preface of the "Mini Symposium on Generalized Inverses and their Applications". In: AIP Conference Proceedings of ICNAAM 2013 (Rhodes, 21–27 September 2013), vol. 1558, p. 1495. - ISBN 978-0-7354-1184-5
  6. KYRCHEI, Ivan: Determinantal Representations of ihe Drazin Inverse Matrix over a Quaternion Skew Field. In: Book of abstracts of International Conference on Algebra dedicated to 100th anniversary of S.M. Chernikov, (Kyiv, August 20-26, 2012)
  7. KYRCHEI, Ivan: Explicit Formulas for Determinantal Representations of the Drazin Inverse Solution of the Quaternion Matrix Equation AXB = D. In: Book of abstracts of 9-th International Algebraic Conference in Ukraine, (L’viv, 8-13 July, 2013)- P. 108
  8. KYRCHEI, Ivan: Explicit Representation Formulas for the Least Squares Solutions of the Quaternion Matrix Equation AXB=D. In: Abstracts of talks of 8-th International Algebraic Conference in Ukraine, (Lugansk, 5-12 July 2011)- P. 171
  9. KYRCHEI, Ivan: Cramer'S Rule for Some Two-Sided Quaternionic Matrix Equations. In: Book of abstracts of 7-th International Algebraic Conference in Ukraine, (Kharkiv, 18-23 August, 2009)- P. 82
  10. KYRCHEI, Ivan: Determinantal Representation of the Moore-Penrose Inverse Matrix over Quaternion Skew Field. In: Book of abstracts of 6-th International Algebraic Conference in Ukraine, (Kamyanets Podilsky, 1-7 July 2007)- P. 120 – 121
  11. KYRCHEI, Ivan: Determinantal Representation of the Inverse Matrix over The Quaternion Skew Field. In: Book of abstracts of 5-th International Algebraic Conference in Ukraine, (Odessa, 20-27June 2005)- P. 120
  12. KYRCHEI, Ivan: The Least Square Solution of System of Linear Equations over the Quaternion Skew Field. In: Abstracts of International Algebraic Conference, (Ekaterinburg, 29.08. – 3.09. 2005)- P. 128-129


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