A remark on the Jordan normal form of matrices
The present paper is a translation of part of an earlier one [Acta Sci. Math. Szeged 17, 190-194 (1956; Zbl 0071.24801)]. Its message is that when considering the normal form of a linear transformation \(A\) on a vector space \(X\) it pays to consider at the same time its adjoint \(A^*\) acting on the dual space. For example, it is shown in this ``geometrical'' way that there exists an \(A\)-invariant direct decomposition \(X = X_s+X_r\), where \(A\) is nilpotent on \(X_s\) and non-singular on \(X_r\).
scientific article; zbMATH DE number 1453245