THE RANGE AND PSEUDO-INVERSE OF A PRODUCT

DOI 3 References
  • SHIJIE LU
    DEPARTMENT OF MATHEMATICS ZHEJIANG UNIVERSITY HANGZHOU PEOPLE'S REPUBLIC OF CHINA

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Abstract

By definition the cosine of the angle between the two subspaces M and N is { \left| {u, v} \ ight|:u \in M, v \in N, \left// u \ ight// = 1 = \left// v \ ight//} . For operators A and B with closed range in Hilbert spaces, AB has closed range if and only if the angle between ker A and B({(\ker AB)^ ⊥ }) is positive. Moreover, if we denote by {A^Ψ } the pseudo-inverse of A, then {(AB)^Ψ } = {B^Ψ }{A^Ψ } if and only if B({(\ker AB)^ ⊥ }) \subset {(\ker A)^ ⊥ } and {A^ * }({(\ker {B^ * }{A^ * })^ ⊥ }) \subset {(\ker {B^ * })^ ⊥ }.

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Details 詳細情報について

  • CRID
    1390282680091478912
  • NII Article ID
    110000026408
  • NII Book ID
    AA00863953
  • DOI
    10.2748/tmj/1178228371
  • ISSN
    2186585X
    00408735
  • MRID
    876455
  • Text Lang
    en
  • Data Source
    • JaLC
    • Crossref
    • CiNii Articles
  • Abstract License Flag
    Disallowed

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