Upper triangular matrix/Jordan normal matrix/Definition

Jordan normal form

A square matrix of the form

${\begin{pmatrix}J_{1}&0&\cdots &\cdots &0\\0&J_{2}&0&\cdots &0\\\vdots &\ddots &\ddots &\ddots &\vdots \\0&\cdots &0&J_{k-1}&0\\0&\cdots &\cdots &0&J_{k}\end{pmatrix}},$

where each ${}J_{i}$ is a Jordan matrix, is called a matrix in Jordan normal form.