Selfadjoint Endomorphisms

Jonathan S. Golan ()
Additional contact information
Jonathan S. Golan: University of Haifa, Dept. of Mathematics

Chapter 17 in The Linear Algebra a Beginning Graduate Student Ought to Know, 2012, pp 395-418 from Springer

Abstract: Abstract Selfadjoint endomorphisms of inner product spaces are defined and studied. Any selfadjoint endomorphism of a finitely-generated inner product space is shown to have a nonempty spectrum. The notion of orthogonal decomposition of an endomorphism is introduced. Selfadjoint endomorphisms of finitely-generated inner product spaces are shown to be orthogonally diagonalizable, with the converse true for spaces over the real numbers. Positive-definite endomorphisms are introduced and characterized. Application is made to Cholesky decompositions. Isometries of finitely-generated inner product spaces are studied and characterized.

Keywords: Product Space; Diagonal Entry; Symmetric Matrice; Hermitian Matrix; Hermitian Matrice (search for similar items in EconPapers)
Date: 2012
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

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:spr:sprchp:978-94-007-2636-9_17

Ordering information: This item can be ordered from
http://www.springer.com/9789400726369

DOI: 10.1007/978-94-007-2636-9_17

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().