Our aim is to show that for each eigenproblem there is a Lie algebra or a Lie-Poisson structure related to this algebra. Decomposition of the corresponding tensor into simple vectors allows us to find the Casimir function for this structure. By considering a collection of eigenproblems, this procedure can be extended to any Lie algebra. It turns out that this eigenproblem also gives a multiplication on a dual space to a linear space. The dual space with the multiplication comes to be a left-symmetric algebra. The method described in the paper is illustrated by examples of five-dimensional Lie algebra.