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Mathematics, Vol. 8, Pages 830: Numerical Range of Moore–Penrose Inverse Matrices

Research paper by Mao-Ting Chien

Indexed on: 28 May '20Published on: 20 May '20Published in: Mathematics



Abstract

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 ) .