Ascent, descent, nullity, defect, and related notions for linear relations in linear spaces
By Adrian Sandovici, H. D. de Snoo, H. Winkler. 2007
111 citations recorded by the source corpus.
For a linear relation in a linear space the concepts of ascent, descent, nullity, and defect are introduced and studied. It is shown that the results of A.E. Taylor and M.A. Kaashoek concerning the relationship between ascent, descent, nullity, and defect for the case of linear operators remain valid in the context of linear relations, sometimes under the additional condition that the linear relation does not have any nontrivial singular chains. In particular, it is shown for a linear relation A with a trivial singular chain manifold whose ascent p is finite and whose nullity and defect are equal and finite that the linear space h is a direct sum of ker A(p) and ran A(p). Furthermore it is shown that the various results which require the absence of singular chains are not valid when such chains are present. (C) 2007 Elsevier Inc. All rights reserved.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/98c667b9d8e7d0a42d3cb5e18fec503d0cfa6ec7
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In Applied Mathematics
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- An index formula for the product of linear relations (2009, background): “[7]) and they turn out to be the natural tool in the study of indices of linear relations.”
- On the essential spectra of some matrix of linear relations (2014, background): “However, this property is not true in the context of linear relations (see, for example [9]).”