Abstract
An algorithm is offered, which with insignificant modifications permits; 1) the finding of a canonic basis of the root sub space corresponding to a prescribed eigenvalue of a matrix; 2) the finding of chains of associated vectors to the eigenvectors corresponding to a prescribed eigenvalue of a regular linear pencil; 3) the finding of chains of generalized associated vectors corresponding to a prescribed eigenvalue of a regular kernel of a singular linear pencil of complete column rank of two matrices; 4) the finding of linearly independent polynomial solutions of a singular linear pencil. The algorithm consists in the construction of a finite sequence of certain auxiliary matrices the choice of which depends on the problem being solved and in the construction of a sequence of their null-spaces, enabling the obtaining of all necessary information on the unknown vectors of the canonic basis of the problem being solved.
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