proper value

English

Noun

proper value (plural proper values)

1. (dated, linear algebra) An eigenvalue.
   • 1961 [Oxford University Press], Sterling K. Berberian, Introduction to Hilbert Space, American Mathematical Society (AMS Chelsea), 1999, Reprint, page 178,

     In this terminology, Theorem 1 asserts that every non-zero proper value of a CC-operator^{[completely continuous operator]} has finite multiplicity. This result is not always helpful, for there exist CC-operators having no proper values at all:

   • 1962, A. R. Amir-Moéz, A. L. Fass, Elements of Linear Space, Pergamon Press, page 134:

     Thus any proper value of AA* is a proper value of A*A.

   • 2010, F. Takens, A Vanderbauwhede, Local invariant manifolds and normal forms, H. Broer, F. Takens, B. Hasselblatt (editors), Handbook of Dynamical Systems, Volume 3, Elsevier (North-Holland), page 106,

     The proper values of this linear mapping are:

     – the proper values of L;

     – for each proper value α of L|E^c and proper value β of L|E^u, the proper value α/β — from the assumptions it follows that this latter collection of proper values consists of contracting proper values only.

Usage notes

Formerly the standard term in English; replaced by eigenvalue during the course of the 20th century.