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Research Article

Constructing and counting regular triangular matrices

Pages 3936-3943 | Received 08 Sep 2020, Accepted 31 Oct 2020, Published online: 08 Dec 2020

References

  • von Neumann J. On regular rings. Proc Nat Acad Sci. 1936;22:707–713.
  • Meyer CD. Generalized inverses of triangular matrices. SIAM J Appl Math. 1970;18:401–406.
  • Hartwig RE. Robert E. Roth's equivalence problem in unit regular rings. Proc Amer Math Soc. 1976;59:39–44.
  • Baksalary JK, Kala R. The matrix equation AX−Y B = C. Linear Algebra Appl. 1979;25:41–43.
  • Huylebrouck D, Puystjens R. Generalized inverses of a sum with a radical element. Linear Algebra Appl. 1986;84:289–300.
  • Huylebrouck D. The generalized inverse of a sum with a radical element: applications. Linear Algebra Appl. 1996;246:159–175.
  • Patrício P, Puystjens R. About the von Neumann regularity of triangular block matrices. Linear Algebra Appl. 2001;332–334:485–502.
  • Hartwig RE, Patrício P, Puystjens R. Diagonalizing triangular matrices via orthogonal Pierce decompositions. Linear Algebra Appl. 2005;401:381–391.
  • Hartwig RE, Patrício P. On Roth's pseudo equivalence over rings. Electron J Linear Algebra. 2007;16:111–124.
  • Hartwig RE, Patrício P. When does the Moore-Penrose inverse flip? Oper Matrices. 2012;6:181–192.
  • Hou X. Idempotents in triangular matrix rings. Linear Multilinear Algebra. in press, 10.1080/03081087.2019.1596223
  • Wright SE. Triangular idempotent matrices over a general ring. Linear Multilinear Algebra. in press, 10.1080/03081087.2020.1773377

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