The concept of an eigenpolynomial of a linear operator is introduced, an algorithm for the construction of eigenpolynomials is formulated, and a relationship between eigenpolynomials and polynomial invariants of linear loops of programs is established. The main result obtained is the construction of sets of L-invariants for loops of operators whose Jordan forms contain nontrivial blocks.Keywords: static program analysis, polynomial loop invariant, eigenpolynomial of a linear operator, automatic generation problem.

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