• Title, Summary, Keyword: Moore-Penrose inverse

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WEIGHTED MOORE-PENROSE INVERSES OF ADJOINTABLE OPERATORS ON INDEFINITE INNER-PRODUCT SPACES

  • Qin, Mengjie;Xu, Qingxiang;Zamani, Ali
    • Journal of the Korean Mathematical Society
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    • v.57 no.3
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    • pp.691-706
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    • 2020
  • Necessary and sufficient conditions are provided under which the weighted Moore-Penrose inverse AMN exists, where A is an adjointable operator between Hilbert C-modules, and the weights M and N are only self-adjoint and invertible. Relationship between weighted Moore-Penrose inverses AMN is clarified when A is fixed, whereas M and N are variable. Perturbation analysis for the weighted Moore-Penrose inverse is also provided.

CHARACTERIZATIONS AND THE MOORE-PENROSE INVERSE OF HYPERGENERALIZED K-PROJECTORS

  • Tosic, Marina
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.2
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    • pp.501-510
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    • 2014
  • We characterize hypergeneralized k-projectors (i.e., $A^k=A^{\dag}$). 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.

WEIGHTED GDMP INVERSE OF OPERATORS BETWEEN HILBERT SPACES

  • Mosic, Dijana
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.4
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    • pp.1263-1271
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    • 2018
  • We introduce new generalized inverses (named the WgDMP inverse and dual WgDMP inverse) for a bounded linear operator between two Hilbert spaces, using its Wg-Drazin inverse and its Moore-Penrose inverse. Some new properties of WgDMP inverse and dual WgDMP inverse are obtained and some known results are generalized.

The Moore-Penrose Inverse for the Classificatory Models

  • Kim, Byung-Chun;Lee, Jang-Taek
    • Journal of the Korean Statistical Society
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    • v.15 no.1
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    • pp.46-61
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    • 1986
  • Many procedures for deriving the Moore-Penrose invese $X^+$ have been developed, but the explicit forms of Moore-Penerose inverses for design matrices in analysis of variance models are not known heretofore. The purpose of this paper is to find explicit forms of $X^+$ for the one-way and the two-way analysis of variance models. Consequently, the Moore-Penerose inverse $X^+$ and the shortest solutions of them can be easily obtained to the level of pocket calculator by way of our results.

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COMPLETIONS OF HANKEL PARTIAL CONTRACTIONS OF SIZE 5×5 NON-EXTREMAL CASE

  • Lee, Sang Hoon
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.1
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    • pp.137-150
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    • 2016
  • We introduce a new approach that allows us to solve, algorithmically, the contractive completion problem. In this article, we provide concrete necessary and sufficient conditions for the existence of contractive completions of Hankel partial contractions of size $4{\times}4$ using a Moore-Penrose inverse of a matrix.

PERTURBATION ANALYSIS OF THE MOORE-PENROSE INVERSE FOR A CLASS OF BOUNDED OPERATORS IN HILBERT SPACES

  • Deng, Chunyuan;Wei, Yimin
    • Journal of the Korean Mathematical Society
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    • v.47 no.4
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    • pp.831-843
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    • 2010
  • Let $\cal{H}$ and $\cal{K}$ be Hilbert spaces and let T, $\tilde{T}$ = T + ${\delta}T$ be bounded operators from $\cal{H}$ into $\cal{K}$. In this article, two facts related to the perturbation bounds are studied. The first one is to find the upper bound of $\parallel\tilde{T}^+\;-\;T^+\parallel$ which extends the results obtained by the second author and enriches the perturbation theory for the Moore-Penrose inverse. The other one is to develop explicit representations of projectors $\parallel\tilde{T}\tilde{T}^+\;-\;TT^+\parallel$ and $\parallel\tilde{T}^+\tilde{T}\;-\;T^+T\parallel$. In addition, some spectral cases related to these results are analyzed.

RIGHT AND LEFT QUOTIENT OF TWO BOUNDED OPERATORS ON HILBERT SPACES

  • Benharrat, Mohammed
    • Communications of the Korean Mathematical Society
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    • v.35 no.2
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    • pp.547-563
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    • 2020
  • We define a left quotient as well as a right quotient of two bounded operators between Hilbert spaces, and we parametrize these two concepts using the Moore-Penrose inverse. In particular, we show that the adjoint of a left quotient is a right quotient and conversely. An explicit formulae for computing left (resp. right) quotient which correspond to adjoint, sum, and product of given left (resp. right) quotient of two bounded operators are also shown.