Linear relations and their singular chains

Singular chain spaces for linear relations in linear spaces play a fundamental role in the decomposition of linear relations in finite-dimensional spaces. In this paper singular chains and singular chain spaces are discussed in detail for not necessarily finite-dimensional linear spaces. This leads to an identity characterizing a singular chain space in terms of root spaces. The so-called proper eigenvalues of a linear relation play an important role in the finite-dimensional case. 

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