Vladimir V. Sergeichuk

List of publications

  1. Operators on positive semidefinite inner product spaces (with V.A. Bovdi, T. Klymchuk, T. Rybalkina, and M.A. Salim), Linear Algebra Appl. 596 (2020) 82-105.   arXiv

  2. Isometric and selfadjoint operators on a vector space with nondegenerate diagonalizable form (with J.V. Caalim, V. Futorny, and Y. Tanaka), Linear Algebra Appl. 587 (2020) 92-110.   arXiv

  3. New coauthors bring new friends and travels (feature interview; interviewed by R. Horn), Image 63 (2019) 3-6.   pdf

  4. Lipschitz property for systems of linear mappings and bilinear forms (with A. Alazemi, M. Anđelić, and C.M. da Fonseca), Linear Algebra Appl. 573 (2019) 26-36.   arXiv

  5. Wildness for tensors (with V. Futorny and J.A. Grochow), Linear Algebra Appl. 566 (2019) 212-244.   arXiv

  6. Reduction of a pair of skew-symmetric matrices to its canonical form under congruence (with V.A. Bovdi, T.G. Gerasimova, and M.A. Salim), Linear Algebra Appl. 543 (2018) 17-30.   arXiv

  7. Symplectic spaces and pairs of symmetric and nonsingular skew-symmetric matrices under congruence (with V.A. Bovdi, R.A. Horn, and M.A. Salim), Linear Algebra Appl. 537 (2018) 84-99.   arXiv

  8. Wildness of the problems of classifying two-dimensional spaces of commuting linear operators and certain Lie algebras (with V. Futorny, T. Klymchuk, and A.P. Petravchuk), Linear Algebra Appl. 536 (2018) 201-209.   arXiv

  9. Classification of linear mappings between indefinite inner product spaces (with J. Meleiro, T. Solovera, and A. Zaidan), Linear Algebra Appl. 531 (2017) 356-374.   arXiv

  10. Generalization of Roth's solvability criteria to systems of matrix equations (with A. Dmytryshyn, V. Futorny, and T. Klymchuk), Linear Algebra Appl. 527 (2017) 294-302.   arXiv

  11. Specht’s criterion for systems of linear mappings (with V. Futorny and R.A. Horn), Linear Algebra Appl. 519 (2017) 278-295.   arXiv

  12. Topological classification of systems of bilinear and sesquilinear forms (with C.M. da Fonseca, V. Futorny, and T. Rybalkina), Linear Algebra Appl. 515 (2017) 1-5.   arXiv

  13. Neighborhood radius estimation for Arnold’s miniversal deformations of complex and p-adic matrices (with V.A. Bovdi and M.A. Salim), Linear Algebra Appl. 512 (2017) 97-112.   arXiv

  14. Roth’s solvability criteria for the matrix equations AX − \hat{A}B = C and X − A\hat{X}B = C over the skew field of quaternions with an involutive automorphism q → \hat{q} (with V. Futorny and T. Klymchuk), Linear Algebra Appl. 510 (2016) 246-258.   arXiv

  15. Each n-by-n matrix with n >1 is a sum of 5 coninvolutory matrices (with M.N.M. Abara, D.I. Merino, V.I. Rabanovich, J.P. Sta. Maria), Linear Algebra Appl. 508 (2016) 246-254.   arXiv

  16. Topological classification of sesquilinear forms: Reduction to the nonsingular case (with C.M. da Fonseca and T. Rybalkina), Linear Algebra Appl. 504 (2016) 581-589.   arXiv

  17. Tame systems of linear and semilinear mappings and representation-tame biquivers (with T. Klimchuk, D. Kovalenko, and T. Rybalkina), Contemp. Math. 658 (2016) 103-114.   arXiv

  18. Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence (with A. Dmytryshyn, V. Futorny, Bo Kågström, and L. Klimenko), Linear Algebra Appl. 469 (2015) 305-334.   arXiv

  19. Topological classification of oriented cycles of linear mappings (with T. Rybalkina), Ukrainian Math. J. 66 (2015) 1575-1581. arXiv

  20. Consimilarity and quaternion matrix equations AX-\hat{X}B=C, X-A\hat{X}B=C (with T. Klimchuk), Special Matrices 2 (2014) 180-186.   article

  21. Regularizing decompositions for matrix pencils and a topological classification of pairs of linear mappings (with V. Futorny and T. Rybalkina), Linear Algebra Appl. 450 (2014) 121-137.   arXiv

  22. Change of the *congruence canonical form of 2-by-2 matrices under perturbations (with V. Futorny and L. Klimenko), Electr. J. Linear Algebra 27 (2014) 146-154.   article

  23. Miniversal deformations of matrices under *congruence and reducing transformations (with A.R. Dmytryshyn and V. Futorny), Linear Algebra Appl. 446 (2014) 388-420.   arXiv

  24. Symmetric matrix pencils: codimension counts and the solution of a pair of matrix equations (with A. Dmytryshyn and Bo Kågström), Electr. J. Linear Algebra 27 (2014) 1-18.   article

  25. An informal introduction to perturbations of matrices determined up to similarity or congruence (with L. Klimenko), São Paulo J. Math. Sci. 8 (2014) 1-22.   article

  26. Representations of quivers and mixed graphs (with R.A. Horn), Chapter 34 in: L. Hogben (Ed.), Handbook of Linear Algebra, 2nd ed., CRC Press, 2014.   arXiv

  27. Other canonical forms (with R.A. Horn), Chapter 7 in: L. Hogben (Ed.), Handbook of Linear Algebra, 2nd ed., CRC Press, 2014.

  28.  Simultaneous unitary equivalences (with T.G. Gerasimova and R.A. Horn), Linear Algebra Appl. 438 (2013) 3829-3835.   arXiv

  29. Cycles of linear and semilinear mappings (with D. Duarte de Oliveira, V. Futorny, T. Klimchuk, and D. Kovalenko), Linear Algebra Appl. 438 (2013) 3442-3453.   arXiv

  30. Skew-symmetric matrix pencils: Codimension counts and the solution of a pair of matrix equations (with A. Dmytryshyn and Bo Kågström), Linear Algebra Appl. 438 (2013) 3375-3396.   prepr

  31. Systems of subspaces of a unitary space (with V.M. Bondarenko, V. Futorny, T. Klimchuk, and K. Yusenko), Linear Algebra Appl.  438 (2013) 2561-2573.   arXiv

  32. Topological classification of chains of linear mappings (with T. Rybalkina), Linear Algebra Appl.  437 (2012) 860-869.   arXiv

  33. Remarks on the classification of a pair of commuting semilinear operators (with D. Duarte de Oliveira, R.A. Horn, and T. Klimchuk), Linear Algebra Appl. 436 (2012) 3362-3372.   arXiv

  34. Miniversal deformations of matrices of bilinear forms (with A.R. Dmytryshyn and V. Futorny), Linear Algebra Appl. 436 (2012) 2670-2700. arXiv 

  35. Topological classification of Möbius transformations (with T.V. Rybalkina), Fundam. Prikl. Mat. (in Russian) 17 (6) (2011/2012) 175-183. English translation: J. Math. Sci. (N.Y.) 193 (2013) 769-774.  arXiv

  36. A criterion for unitary similarity of upper triangular matrices in general position (with D. Farenick, V. Futorny, T.G. Gerasimova, and N. Shvai), Linear Algebra Appl. 435 (2011) 1356-1369.   arXiv

  37. A canonical form for nonderogatory matrices under unitary similarity (with V. Futorny and R.A. Horn), Linear Algebra Appl. 435 (2011) 830-841.   arXiv

  38. Block triangular miniversal deformations of matrices and matrix pencils (with L. Klimenko), in: V. Olshevsky, E. Tyrtyshnikov (Eds), Matrix Methods: Theory, Algorithms and Applications, World Sci. Publ., Hackensack, NJ, 2010, pp. 69-84.   arXiv

  39. Matrices that are self-congruent only via matrices of determinant one (with T.G. Gerasimova and R.A. Horn), Linear Algebra Appl. 431 (2009) 1620-1632.   arXiv

  40. Canonical forms for unitary congruence and *congruence (with R.A. Horn), Linear Multilinear Algebra 57 (2009) 777-815.   arXiv

  41. Problems of classifying associative or Lie algebras over a field of characteristic not two and finite metabelian groups are wild (with G. Belitskii, A.R. Dmytryshyn, R. Lipyanski, and A. Tsurkov) Electr. J. Linear Algebra 18 (2009) 516-529.   article

  42. Preface [Special issue in honor of Thomas J. Laffey] (with R. Gow, R. Loewy, J.F. Queiró), Linear Algebra Appl. 430 (2009) 1725-1729.

  43. Pairs of mutually annihilating operators (with V.M. Bondarenko and T.G. Gerasimova), Linear Algebra Appl. 430 (2009) 86-105.   arXiv

  44. Normal form of m-by-n-by-2 matrices for equivalence (with G. Belitskii and M. Bershadsky), J. Algebra 319 (2008) 2259-2270.   arXiv

  45. Tridiagonal canonical matrices of bilinear or sesquilinear forms and of pairs of symmetric, skew-symmetric, or Hermitian forms (with V. Futorny and R.A. Horn), J. Algebra 319 (2008) 2351-2371.   arXiv

  46. Canonical matrices of isometric operators on indefinite inner product spaces, Linear Algebra Appl. 428 (2008) 154-192.   arXiv

  47. Canonical matrices of bilinear and sesquilinear forms (with R.A. Horn), Linear Algebra Appl. 428 (2008) 193-223.   arXiv

  48. Classification of squared normal operators on unitary and Euclidean spaces (with V. Futorny and R.A. Horn), Fundam. Prikl. Mat. 13 (no. 4) (2007) 225-232 (in Russian). English translation: J. Math. Sci. (N.Y.) 155 (2008) 950-955.   Rus  arXiv

  49. Linearization method in classification problems of linear algebra, São Paulo J. Math. Sci. 1 (2007) 219-240.

  50. Classification of sesquilinear forms with the first argument on a subspace or a factor space (with V. Futorny), Linear Algebra Appl. 424 (2007) 282-303.   arXiv

  51. Positivity criteria generalizing the leading principal minors criterion (with V. Futorny and N. Zharko), Positivity 11 (no. 1) (2007) 191-199. arXiv

  52. A regularization algorithm for matrices of bilinear and sesquilinear forms (with R.A. Horn), Linear Algebra Appl. 412 (2006) 380-395.   arXiv

  53. Rigid systems of second-order linear differential equations (with M.I. Garcia-Planas, M.D. Magret, and N.A. Zharko), Linear Algebra Appl. 414 (2006) 517-532.   arXiv

  54. Canonical forms for complex matrix congruence and *congruence (with R.A. Horn), Linear Algebra Appl. 416 (2006) 1010-1032.   arXiv

  55. Congruence of multilinear forms (with G. Belitskii), Linear Algebra Appl. 418 (2006) 751-762.   arXiv

  56. Canonical Matrices and Related Questions, Proceedings of Institute of Mathematics of NAS of Ukraine. Mathematics and its Applications, Vol. 57, Kiev, 2006, 326 p.   book

  57. Miniversal deformations of chains of linear mappings (with T.N. Gaiduk and N.A. Zharko), Algebra Discrete Math. (no.1) (2005) 47-61.  pdf  arXiv

  58. The problems of classifying pairs of forms and local algebras with zero cube radical are wild (with G. Belitskii, V.M. Bondarenko, R. Lipyanski, and V.V. Plachotnik), Linear Algebra Appl. 402 (2005) 135-142.   arXiv

  59. Solution of linear matrix equations in a *congruence class (with R.A. Horn and N. Shaked-Monderer), Electr. J. Linear Algebra 13 (2005) 153-156.   article

  60. Problems of classifying associative or Lie algebras and triples of symmetric or skew-symmetric matrices are wild (with G. Belitskii and R. Lipyanski), Linear Algebra Appl. 407 (2005) 249-262.   arXiv

  61. Computation of canonical matrices for chains and cycles of linear mappings, Linear Algebra Appl. 376 (2004) 235-263.   arXiv

  62. Generic canonical form of pairs of matrices with zeros (with T. Gaiduk), Linear Algebra Appl. 380 (2004) 241-251.   arXiv

  63. Congruences of a square matrix and its transpose (with R.A. Horn), Linear Algebra Appl. 389 (2004) 347-353.   arXiv

  64. Complexity of matrix problems (with G. Belitskii), Linear Algebra Appl. 361 (2003) 203-222.   arXiv

  65. Estimate of the number of one-parameter families of modules over a tame algebra (with T. Bruestle), Linear Algebra Appl. 365 (2003) 115-133.   arXiv

  66. Generic families of matrix pencils and their bifurcation diagrams (with M.I. Garcia-Planas), Linear Algebra Appl. 332/334 (2001) 165-179. arXiv

  67. Canonical matrices for linear matrix problems, Linear Algebra Appl. 317 (2000) 53-102.   arXiv

  68. Simplest miniversal deformations of matrices, matrix pencils, and contragredient matrix pencils (with M.I. Garcia-Planas), Linear Algebra Appl. 302/303 (1999) 45-61.   arXiv

  69. Littlewood's algorithm and quaternion matrices (with D.I. Merino), Linear Algebra Appl. 298 (1999) 193-208.   arXiv

  70. Unitary and Euclidean representations of a quiver, Linear Algebra Appl. 278 (1998) 37-62.   arXiv

  71. On subgroups lifting modulo central commutant, Ukrainian Math. J. 50 (no. 5) (1998) 842-845.   pdf

  72. Elementary and multi-elementary representations of vectroids (with K.I. Belousov, L.A. Nazarova, and A.V. Roiter), Ukrainian Math. J. 47 (no. 11) (1995) 1661-1687.   pdf

  73. Existence of a multiplicative basis for a finitely spaced module over an aggregate (with A.V. Roiter), Ukrainian Math. J. 46 (no. 5) (1994) 604-617.   pdf

  74. Classification of pairs of linear operators in a four-dimensional vector space (with D.V. Galinskii), Infinite groups and related algebraic structures, Akad. Nauk Ukrainy, Inst. Mat., Kiev, 1993, 413-430 (in Russian).   MathRev. pdf

  75. Tame and wild subspace problems (with P. Gabriel, L.A. Nazarova, A.V. Roiter, and D. Vossieck), Ukrainian Math. J. 45 (no. 3) (1993) 335-372.   pdf

  76. Classification of sesquilinear forms, pairs of Hermitian forms, and selfadjoint and isometric operators over the field of quaternions, Math. Notes 49 (no. 3–4 ) (1991) 409-414.   MathRev

  77. A note on classification of holomorphic matrices up to similarity, Funct. Anal. Appl. 25 (no. 2) (1991) 135.   pdf

  78. Symmetric representations of algebras with involution, Math. Notes 50 (no. 3-4) (1991) 1058-1061.   pdf

  79. Classification of pairs of subspaces in spaces with scalar product, Ukrainian Math. J. 42 (no. 4) (1990) 487-491.   pdf

  80. Pseudolinear matrix pencils and systems of linear differential equations with meromorphic coefficients, Differential Equations 25 (no. 10) (1989) 1201-1206.  pdf

  81. Classification problems for systems of forms and linear mappings, Math. USSR–Izv. 31 (no. 3) (1988) 481-501.   arXiv   pdf

  82. Holomorphic equivalence of a system of linear differential equations with meromorphic coefficients to a system with linear fractional coefficients, Differentsialnye Uravneniya 24 (no. 6) (1988) 1064-1066 (in Russian).   MathRev

  83. Metric representations of a quiver (with H.M. Havidi), Dokl. Akad. Nauk Ukrain. SSR Ser. A (no. 12) (1988) 19-21 (in Russian).   MathRev

  84. Two semiclassifying theorems for metabelian groups (with H.M. Hawidi), Delta J. Sci. 12 (no. 1) (1988) 31-43.   MathRev

  85. The canonical form of the matrix of a bilinear form over an algebraically closed field of characteristic 2, Math. Notes 41 (no. 5-6) (1987) 441-445.   pdf

  86. Classification problems for systems of linear mappings and sesquilinear forms, Kiev State University, 1983, 60 p. = Manuscript No. 196 Uk–D84, deposited at the Ukrainian NIINTI, 1984 (in Russian); R. Zh. Mat. 1984, 7A331.   pdf

  87. Classification of linear operators in a finite-dimensional unitary space, Functional Anal. Appl. 18 (no. 3) (1984) 224-230.   pdf

  88. Representation of dischemes, Linear algebra and the theory of representations, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1983, 110-134 (in Russian).   MathRev

  89. Representations of simple involutive quivers, Representations and quadratic forms, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1979, 127-148 (in Russian).   MathRev

  90. Finitely generated groups with commutator group of prime order. Ukrainian Math. J. 30 (no. 6) (1978) 592-598.   pdf

  91. The classification of metabelian p-groups, Matrix problems, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1977, 150-161 (in Russian).   MathRev

  92. Application of modules over a dyad for the classification of finite p-groups possessing an abelian subgroup of index p and of pairs of mutually annihilating operators (with L.A. Nazarova, A.V. Roiter, and V.M. Bondarenko), Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. 28 (1972) 69-92 (in Russian). English translation: J. Soviet Math. 3 (1975) 636-654.   pdf