Algebraic properties of generalized inverses

• 作者： Cvetkovic-Ilic, Dragana S., author.
• 其他作者：
  • Wei, Yimin, author.
  • SpringerLink (Online service)
• 其他題名：
  • Developments in mathematics ;
• 出版： Singapore : Springer Singapore :Imprint: Springer
• 叢書名： Developments in mathematics,volume 52
• 主題： Linear operators--Generalized inverses. , Mathematics. , Linear and Multilinear Algebras, Matrix Theory.
• ISBN： 9789811063497 (electronic bk.) 、 9789811063480 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: Definitions and motivations -- Reverse order law -- Completions of operator matrices and generalized inverses -- Generalized inverses and idempotents -- Drazin inverse of a 2 × 2 block matrix -- Additive Results for the Drazin Inverse -- Index.
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• 摘要註: This book addresses selected topics in the theory of generalized inverses. Following a discussion of the "reverse order law" problem and certain problems involving completions of operator matrices, it subsequently presents a specific approach to solving the problem of the reverse order law for {1} -generalized inverses. Particular emphasis is placed on the existence of Drazin invertible completions of an upper triangular operator matrix; on the invertibility and different types of generalized invertibility of a linear combination of operators on Hilbert spaces and Banach algebra elements; on the problem of finding representations of the Drazin inverse of a 2x2 block matrix; and on selected additive results and algebraic properties for the Drazin inverse. In addition to the clarity of its content, the book discusses the relevant open problems for each topic discussed. Comments on the latest references on generalized inverses are also included. Accordingly, the book will be useful for graduate students, PhD students and researchers, but also for a broader readership interested in these topics.
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