Invariant subspaces
Identifieur interne : 003540 ( Main/Exploration ); précédent : 003539; suivant : 003541Invariant subspaces
Auteurs : Werner H. Greub [Canada]Source :
- Die Grundlehren der Mathematischen Wissenschaften [ 0072-7830 ] ; 1963.
Abstract
Abstract: The eigenvalue problem concerns itself with the following question : Given an endomorphism σ of a linear space E find all the 1-dimensional invariant linear subspace, i. e. all vectors x for which σx = λx. In Chapter IV, § 5 we found that an endomorphism need not have eigenvectors. Therefore it is natural to generalize the problem by admitting invariant subspaces of higher dimension, i. e. by asking for linear sub-spaces E 1 of E with the property that σ E⊂1 E 1. Obviously the whole space E as well as the kernel of σ are such subspaces. In order to exclude trivial cases in the investigation of this question it will be necessary to require that the invariant subspaces are irreducible, i. e. that they can not be decomposed any further into invariant subspaces.
Url:
DOI: 10.1007/978-3-662-01545-2_15
Affiliations:
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