Numerical Range of Moore–Penrose Inverse Matrices

Mao-Ting Chien
Additional contact information
Mao-Ting Chien: Department of Mathematics, Soochow University, Taipei 111002, Taiwan

Mathematics, 2020, vol. 8, issue 5, 1-8

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 ) .

Keywords: Moore–Penrose inverse; numerical range; weighted shift matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/5/830/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/5/830/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:5:p:830-:d:360664

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().