The expression of Moore--Penrose inverse of A-XY^*

2010/03/08 by Fapeng Du, Du, Fapeng, Yifeng Xue +1
Computer Science · Mathematics · #47A05 #65F20 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1003.1602

openalex publication_date 2010/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K, H be Hilbert spaces and let L(K,H) denote the set of all bounded linear operators from K to H. Let A ∈ L(H)\triangleq L(H,H) with R(A) closed and X,Y ∈ L(K,H) with R(X)⊆ R(A),R(Y)⊆ R(A^*). In this short note, we give some new expressions of the Moore--Penrose inverse (A-XY^*)⁺ of A-XY^* under certain suitable conditions.

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