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Numerical Range of Moore–Penrose Inverse Matrices

Department of Mathematics, Soochow University, Taipei 111002, Taiwan
Mathematics 2020, 8(5), 830; https://doi.org/10.3390/math8050830
Received: 29 April 2020 / Revised: 16 May 2020 / Accepted: 19 May 2020 / Published: 20 May 2020
(This article belongs to the Section Computational Mathematics)
Let A be an n-by-n matrix. The numerical range of A is defined as W ( A ) = { x * A x : x C n , x * x = 1 } . The Moore–Penrose inverse A + of A is the unique matrix satisfying A A + A = A , A + A A + = A + , ( A A + ) * = A A + , and ( A + A ) * = A + A . This paper investigates the numerical range of the Moore–Penrose inverse A + of a matrix A, and examines the relation between the numerical ranges W ( A + ) and W ( A ) . View Full-Text
Keywords: Moore–Penrose inverse; numerical range; weighted shift matrix Moore–Penrose inverse; numerical range; weighted shift matrix
MDPI and ACS Style

Chien, M.-T. Numerical Range of Moore–Penrose Inverse Matrices. Mathematics 2020, 8, 830.

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