On nilpotent matrices. (Russian) Zbl 0602.15019

Ufnarovskij, V. A.; Chekanu, G. P.

Mat. Issled. 85, 130-141 (1985).

The authors pursue a pedagogical objective: to present some well-known facts about nilpotent matrices and nilpotent algebras of matrices in clearly understandable form and from different points of view. The first section treats some results dealing with ranks, indices of nilpotency, images, invariant subspaces of nilpotent matrices, etc. from the viewpoint of linear transformations of linear spaces while the second section treats them from the viewpoint of ring theory.

Reviewer: B.Reichstein

MSC:

15B57	Hermitian, skew-Hermitian, and related matrices
15A04	Linear transformations, semilinear transformations
15A30	Algebraic systems of matrices
16S50	Endomorphism rings; matrix rings

Keywords:

nilpotent matrices; nilpotent algebras; invariant subspaces; linear transformations; linear spaces