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A note on the representation and definition of semiseparable matrices
Author(s) -
Vandebril Raf,
Van Barel Marc,
Mastronardi Nicola
Publication year - 2005
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.455
Subject(s) - tridiagonal matrix , representation (politics) , mathematics , matrix representation , class (philosophy) , generator (circuit theory) , algebra over a field , pure mathematics , computer science , eigenvalues and eigenvectors , power (physics) , group (periodic table) , physics , organic chemistry , quantum mechanics , artificial intelligence , politics , political science , law , chemistry
In this paper the definition of semiseparable matrices is investigated. Properties of the frequently used definition and the corresponding representation by generators are deduced. Corresponding to the class of tridiagonal matrices another definition of semiseparable matrices is introduced preserving the nice properties dual to the class of tridiagonal matrices. Several theorems and properties are included showing the viability of this alternative definition. Because of the alternative definition, the standard representation of semiseparable matrices is not satisfying anymore. The concept of a representation is explicitly formulated and a new kind of representation corresponding to the alternative definition is given. It is proved that this representation keeps all the interesting properties of the generator representation. Copyright © 2005 John Wiley & Sons, Ltd.