JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (5): 100-106.doi: 10.6040/j.issn.1671-9352.0.2023.383

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Numerical range of Moore-Penrose inverses of a combination of two orthogonal projections

WANG Ran, YU Weiyan*   

  1. College of Mathematics and Statistics, Hainan Normal University, Haikou 571158, Hainan, China
  • Published:2025-05-19

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Abstract: Let H be a complex separable Hilbert space, and P and Q be two orthogonal projection operators on H. This article mainly studies the numerical range of the Moore-Penrose inverse operator(P+QP)† of the combination of P and Q. By using the operator block technique, the geometric characterization of the numerical range of the operator(P+QP)† is given. That is, the closure of its numerical range is a closed convex hull of some explicit ellipses parameterized by points in the spectrum of operator PQ.

Key words: numerical range, orthogonal projections, Moore-Penrose inverse, support function

CLC Number: 

  • O177.1
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