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Characterizations and the Moore-Penrose inverse of hypergeneralized k-projectors

Marina Tosic
대한수학회 (The Korean Mathematical Society)|2014.03|대한수학회보 (Bulletin of the KMS)|제51권 제2호|pp. 501-510

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참고문헌

키워드

linear combinationhypergeneralized k-projectorthe Moore-Penrose inversenonsingularity
주제분류수학

초록

We characterize hypergeneralized k-projectors (i.e., Ak = A†). Also, some representation for the Moore-Penrose inverse of a linear combination of hypergeneralized k-projectors is found and the invertibility for some linear combinations of commuting hypergeneralized k-projectors is considered.

Abstract

We characterize hypergeneralized k-projectors (i.e., Ak = A†). Also, some representation for the Moore-Penrose inverse of a linear combination of hypergeneralized k-projectors is found and the invertibility for some linear combinations of commuting hypergeneralized k-projectors is considered.

참고문헌 (14)

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  8. S. L. Campbell, "Generalized Inverses of Linear Transformations" (1979), Pitman
  9. C. Y. Deng, "Generalized n-idempotents and Hyper-generalized n-idempotents", Northeast. Math. J, 22(4), pp.387~394 (2006)
  10. T. N. E. Greville, "Note on the generalized inverse of a matrix product", SIAM Rev, 8, pp.518~521 (1966)
  11. J. Groß, "Generalized and hypergeneralized projectors", Linear Algebra Appl, 264, pp.463~474 (1997)
  12. R. E. Hartwig, "Matrices for which A∗ and A† commute", Linear Multilinear Algebra, 14(3), pp.241~256 (1983)
  13. M. Toˇsi´c, "The invertibility of the difference and the sum of commuting generalized and hypergeneralized projectors", Linear Multilinear Algebra, 61(4), pp.482~493 (2013)
  14. M. Toˇsi´c, "The Moore-Penrose inverse of a linear com-bination of commuting generalized and hypergeneralized projectors", Electron. J. Linear Algebra, 22, pp.1129~1137 (2011)

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