JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (2): 37-42.doi: 10.6040/j.issn.1671-9352.0.2024.194

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Spectral decomposition of the Moore-Penrose inverse of operator with closed range

PANG Yongfeng, DU Yawei, YUE Huihui   

  1. School of Science, Xian University of Architecture and Technology, Xian 710055, Shaanxi, China
  • Published:2026-02-13

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Abstract: First, this paper proves the equivalence among several definitions of the Moore-Penrose inverse of an operator. Second, by utilizing the spectral decomposition of a self-adjoint operator, we provide the spectral decomposition of the Moore-Penrose inverse of an operator with a closed range. Finally, by employing the Moore-Penrose inverse of an operator, we offer a general representation of the best approximation set, thereby proving that the best approximation set is an affine manifold.

Key words: Moore-Penrose inverse of operator, spectral decomposition, affine manifolds

CLC Number: 

  • O177
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