Geodesic
Principal vectors of a nonlinear finite-dimensional eigenvalue problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 2, pp. 187-192

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In a finite-dimensional linear space, consider a nonlinear eigenvalue problem analytic with respect to its spectral parameter. The notion of a principal vector for such a problem is examined. For a linear eigenvalue problem, this notion is identical to the conventional definition of principal vectors. It is proved that the maximum number of linearly independent eigenvectors combined with principal (associated) vectors in the corresponding chains is equal to the multiplicity of an eigenvalue. A numerical method for constructing such chains is given. 
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A. A. Abramov; L. F. Yukhno. Principal vectors of a nonlinear finite-dimensional eigenvalue problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 2, pp. 187-192. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_2_a0/