Linear mapping/Trigonalizable/Via upper triangular form/Definition

Trigonalizable mapping

Let ${}K$ denote a field, and let ${}V$ denote a finite-dimensional vector space. A linear mapping ${}\varphi \colon V\rightarrow V$ is called trigonalizable, if there exists a basis such that the describing matrix of ${}\varphi$ with respect to this basis is an upper triangular matrix.