Jordan matrix/Above/Definition

Let ${\displaystyle {}K}$ be a field and ${\displaystyle {}\lambda \in K}$. A Jordan matrix (to the eigenvalue ${\displaystyle {}\lambda }$) is a square matrix of the form

${\displaystyle {\begin{pmatrix}\lambda &1&0&\cdots &\cdots &0\\0&\lambda &1&0&\cdots &0\\\vdots &\ddots &\ddots &\ddots &\ddots &\vdots \\0&\cdots &0&\lambda &1&0\\0&\cdots &\cdots &0&\lambda &1\\0&\cdots &\cdots &\cdots &0&\lambda \end{pmatrix}}.}$