Ivan Igorovych Kyrchei

Personal page

An institute which one has graduated - Ivan Franko National University of Lviv
Year of graduation - 1992
Specialty - mathematics

Title, academic degree - Senior Reseach Fellow; Doctor of Physical and Mathematical Sciences, Ph.D.,

Post - Leading Reseacher

Major research interests:

Books:

  • I.I. Kyrchei (Ed.), Generalized Inverses: Algorithms and Applications. New York: Nova Sci. Publ., 2022. ISBN: 978-1-68507-356-5. SENSE (C)
  • I.I. Kyrchei (Ed.), Hot Topics in Linear Algebra. New York: Nova Sci. Publ., 2020. ISBN: 978-1-53617-770-1. SENSE (C)
  • I.I. Kyrchei (Ed.), Advances in Linear Algebra Research. New York: Nova Sci. Publ., 2015. ISBN: 978-1-63463-565-3. SENSE (C)

    • Major publications:

    1. I.I. Kyrchei, Cramer's rules for systems of quaternion matrix equations. In: Ivan I. Kyrchei (Ed.), “Generalized Inverses: Algorithms and Applications”, pp. 95-168. New York: Nova Sci. Publ., 2022.
    2. ².². Kyrchei, D. Mosic, P.S. Stanimirovic, MPD-DMP-solutions to quaternion two-sided restricted matrix equations, Computational and Applied Mathematics 40: 177 (2021). [Q2]
    3. H. Ma, P.S. Stanimirovic, D. Mosic, I.I. Kyrchei, Weighted minimization problems for quaternion matrices, Applied Mathematics and Computation 404: 126247 (2021).[Q1]
    4. A. Rehman, I. Kyrchei, M. Akram, I. Ali, A. Shakoor, Explicit formulas and determinantal representation for $\eta$-skew-Hermitian solution to a system of quaternion matrix equations, Iranian Journal of Science and Technology, Transactions A: Science 45(3), 1015-1024. (2021)[Q2]
    5. ².². Kyrchei, D. Mosic, P.S. Stanimirovic, Weighted minimization problems for quaternion matrices, Advances in Applied Clifford Algebras, 31: 48 (2021).[Q3]
    6. D. Mosic, ².². Kyrchei, P.S. Stanimirovic, Representations and properties for the MPCEP inverse, Journal of Applied Mathematics and Computing, (2021). [Q2]
    7. ².². Kyrchei, D. Mosic, P.S. Stanimirovic, Solvability of new constrained quater-nion matrix ap proximation problems based on core-EP inverses, Advances in Applied Clifford Algebras, 31:3 (2021). [Q2]
    8. I.I. Kyrchei, Determinantal representations of solutions to systems of two-sided quaternion matrix equations Linear and Multilinear Algebra, 69(4), 648-672 (2021). [Q2]
    9. I.I. Kyrchei, Weighted quaternion core-EP, DMP, MPD, and CMP inverses and their determinantal representations, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matemfticas, 114:198 (2020). [Q2]
    10. A. Rehman, I. Kyrchei, M. Akram, I. Ali, A. Shakoor, Explicit formulas and determinantal representation for $\eta$-skew-Hermitian solution to a system of quaternion matrix equations, Filomat, 34(8), 2601-2627 (2020). [Q2]
    11. I.I. Kyrchei, Cramer's rules for Sylvester-type matrix equations. In: I. Kyrchei (Ed.), Hot Topics in Linear Algebra, pp. 45-110. New York: Nova Sci. Publ., 2020. [SENSE C]
    12. A. Rehman, I. Kyrchei, M. Akram, I. Ali, A. Shakoor, System of mixed generalized Sylvester-type quaternion matrix equations. In: I. Kyrchei (Ed.), Hot Topics in Linear Algebra, pp. 138-162. New York: Nova Sci. Publ., 2020.[SENSE C]
    13. I.I. Kyrchei, Determinantal representations of the weighted core-EP, DMP, MPD, and CMP inverses, Journal of Mathematics, Article ID 9816038, 12 p., (2020). [Q3]
    14. I.I. Kyrchei, Determinantal representations of the core inverse and its generalizations, In: Functional Calculus, London: IntechOpen, 2019. [SENSE D]
    15. I.I. Kyrchei, Cramer’s rules of \eta-(skew-) Hermitian solutions to the quaternion Sylvester-type matrix equations, Advances in Applied Clifford Algebras, 29(3): 56 (2019). [Q3]
    16. I.I. Kyrchei, Determinantal representations of the quaternion core inverse and its generalizations, Advances in Applied Clifford Algebras, 29: 104 (2019). [Q3]
    17. I.I. Kyrchei, Determinantal representations of the core inverse and its generalizations with applications, Journal of Mathematics, ID 1631979, 13 p., (2019). [Q3]
    18. A. Rehman, I. Kyrchei, M. Akram, I. Ali, A. Shakoor, Least-norm of the general solution to some system of quaternion matrix equations and its determinantal representations, Abstract and Applied Analysis, ID 907269, 18 p., (2019). [Q4]
    19. A. Rehman, I. Kyrchei, M. Akram, I. Ali, A. Shakoor, The general solution of quaternion matrix equation having \eta-Skew-Hermicity and its Cramer’s rule, Mathematical Problems in Engineering, ID 7939238, 25 p., (2019). [Q3]
    20. I.I. Kyrchei, Cramer’s rules for the system of quaternion matrix equations with \eta-Hermicity, 4open, 2:24 (2019).
    21. I.I. Kyrchei, Determinantal representations of general and (skew-)Hermitian solutions to the generalized Sylvester-type quaternion matrix equation, Abstract and Applied Analysis, Article ID 5926832, 14 p., (2019). [Q4]
    22. I.I. Kyrchei, Cramer’s rules for Sylvester quaternion matrix equation and its special cases, Advances in Applied Clifford Algebras, 28(5):90 (2018). [Q3]
    23. I.I. Kyrchei, Determinantal representations of solutions to systems of quaternion matrix equations, Advances in Applied Clifford Algebras, 28(1):23 (2018). [Q3]
    24. I.I. Kyrchei, Determinantal representations of solutions and Hermitian solutions to some system of two-sided quaternion matrix equations, Journal of Mathematics, Article ID 6294672, (2018), 12 p. [Q4]
    25. I.I. Kyrchei, Explicit determinantal representation formulas for the solution of the two-sided restricted quaternionic matrix equation, Journal of Applied Mathematics and Computing, 58(1-2), 335-365 (2018). [Q3]
    26. I.I. Kyrchei, Cramer’s rules for the system of two-sided matrix equations and of its special cases. In: H.A. Yasser (Ed.), Matrix Theory-Applications and Theorems, pp. 3-20. IntechOpen, 2018. [SENSE D]
    27. I.I. Kyrchei, Weighted singular value decomposition and determinantal representations of the quaternion weighted Moore–Penrose inverse, Applied Mathematics and Computation, 309, 1-16 (2017). [Q1]
    28. I.I. Kyrchei, Cramer’s Rules for some Hermitian coquaternionic matrix equations, Advances in Applied Clifford Algebras, 27(3), 2509–2529 (2017). [Q2]
    29. I. Kyrchei, Determinantal representations for the solution of the generalized Sylvester quaternion matrix equation, Journal of Mathematical Sciences, (2020), 246, 234-244.
      DOI:10.1007/s10958-020-04733-0. Translated from: Mat. Metody Fiz.-Mekh. Polya, 60(3) (2017), pp. 97-106. (in Ukrainian).
    30. I. Kyrchei, Explicit representation formulas for solutions to systems of quaternion matrix equations. Nonclassical problems of the theory of differential equations: a collection of scientific works, devoted to the 80th anniversary of B. Y. Ptashnik, p.110-123. - Lviv: Pidstryhach IAPMM of the National Academy of Sciences of Ukraine, 2017 (in Ukrainian).
    31. I.I. Kyrchei, Determinantal representations of the quaternion weighted Moore-Penrose inverse and its applications. In: Albert R. Baswell (Ed.): Advances in Mathematics Research 23, pp. 35-96. New York: Nova Sci. Publ., 2017. [SENSE C]
    32. I.I. Kyrchei, 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, pp.201-275. New York: Nova Sci. Publ., 2017. [SENSE C]
    33. M. Hajarian, J.Yuan, I. Kyrchei, Applications of methods of numerical linear algebra in engineering 2016, Mathematical Problems in Engineering, Article ID 4854759, 2 p., (2016). [Q3]
    34. I.I. Kyrchei, Explicit determinantal representation formulas of W-weighted Drazin inverse solutions of some matrix equations over the quaternion skew field, Mathematical Problems in Engineering, Article ID 8673809, 13 p., (2016). [Q3]
    35. I.I. Kyrchei, The column and row immanants of matrices over a split quaternion algebra, Advances in Applied Clifford Algebras, 25, 611-619 (2015). [Q3]
    36. I.I. Kyrchei, Determinantal representations of the W-weighted Drazin inverse over the quaternion skew field, Applied Mathematics and Computation, 264, 453–465 (2015). [Q2]
    37. I.I. Kyrchei, Cramer's Rule for Generalized Inverse Solutions. In: Ivan I. Kyrchei, (Ed.): Advances in Linear Algebra Research, pp. 79-132. New York: Nova Sci. Publ., 2015.[SENSE C]
    38. A. Kleyn, Ivan Kyrchei, Relation of Row-Column Determinants with Quasideterminants of Matrices over a Quaternion Algebra. In: Ivan KYRCHEI, (Ed.): Advances in Linear Algebra Research, pp.299-324. New York: Nova Sci. Publ., 2015.[SENSE C]
    39. I.I. Kyrchei, Determinantal representations of the Drazin inverse over the quaternion skew field with applications to some matrix equations, Applied Mathematics and Computation, 238, 193-207 (2014).[Q2]
    40. I.I. Kyrchei, Explicit formulas for determinantal representations of the Drazin inverse solutions of some matrix and differential matrix equations, Applied Mathematics and Computation, 219, 7632-7644 (2013). [Q1]
    41. I.I. Kyrchei, Explicit representation formulas for the minimum norm least squares solutions of some quaternion matrix equations, Linear Algebra and Its Applications, 438(1), 136–152 (2013). [Q1]
    42. I.I. Kyrchei, The theory of the column and row determinants in a quaternion liear algebra, Advances in Mathematics Research 15, pp. 301-359. Nova Sci. Publ., New York, 2012. [SENSE C]
    43. I.I. Kyrchei, Analogs of Cramer's rule for the minimum norm least squares solutions of some matrix equations, Applied Mathematics and Computation, 218, 6375-6384 (2012).[Q1]
    44. I.I. Kyrchei, Determinantal representations of the Moore-Penrose inverse over the quaternion skew field and corresponding Cramer's rules, Linear and Multilinear Algebra 59(4), 413-431 (2011).[Q2]
    45. I. I.Kyrchei, Cramer's rule for some quaternion matrix equations, Applied Mathematics and Computation, 217(5), 2024-2030 (2010). [Q2]
    46. Determinantal representation of the Moore-Penrose inverse matrix over the quaternion skew field, Journal of Mathematical Sciences 180(1) 23-33 (2012).[Q3]
      Translated from Mat. Metody Fiz.-Mekh. Polya. 53(3) (2010), pp.36-46.
    47. I.I. Kyrchei, Analogs of the adjoint matrix for generalized inverses and corresponding Cramer rules, Linear and Multilinear Algebra 56(4), 453–469 (2008).[Q2]
    48. I.I. Kyrchei, [ Cramer’s rule for quaternionic systems of linear equations, Journal of Mathematical Sciences 155(6) 839-858, (2008)[Q4]
      Translated from Fundamentalnaya i Prikladnaya Matematika, 13(4) (2007), pp. 67-94.
    49. I. I.Kyrchei, Cramer rule over quaternion division algebra, Bulletin of the University of Kiev. Series: Physics and Mathematics, 1 (2006), pp.28-34 (in Ukrainian).
    50. I. I.Kyrchei, Determinantal representation of the Drazin inverse. Mathematical Methods and Physicomechanical Fields, 49(2) (2006), pp.58-64. (in Ukrainian).
    51. I. I. Kyrchei, Representation of generalized inverse Moore-Penrose matrix by analog of classical adjoint matrix. Mathematical Methods and Physicomechanical Fields, 47(4) (2004), pp.6-11. (in Ukrainian).
    52. I.I.Kyrchei, Analogue of adjoint matrix over skew field with involution. Mathematical Methods and Physicomechanical Fields, 46(4) (2003), pp.81-91 (in Ukrainian).
    53. I. Kyrchey, The inverse matrix for hermitian over a quasi-field, Visnyk Lviv Univ. Ser. Appl. Math. Comp. Sci., 4 (2002), pp. 120-125 (in Ukrainian).
    54. I. I.Kyrchei, Classical adjoint for Hermitian matrix over quasi-field, Mathematical Methods and Physicomechanical Fields, 44(3) (2001), pp.33-49 (in Ukrainian).
    55. I.I. Kirchei, Fractional-rational regularization of a system of linear equations over the skew-field of quaternions, Journal of Mathematical Sciences 90(5) 2398-2403, (1998)[Q4]
      Translated from Mat. Metody Fiz.-Mekh. Polya 39(2) (1996), pp.89-95 (in Ukrainian).

    E-mail addresses - kyrchei@lms.lviv.ua, kyrchei@online.ua, st260664@gmail.com, ivankyrchei26@gmail.com