Jordan matrix

In the mathematical discipline of matrix theory, a Jordan matrix, named after Camille Jordan, is a block diagonal matrix over a ring R (whose identities are the zero (0) and one (1)), where each block along the diagonal, called a Jordan block, has the following form: $${\displaystyle {\begin{bmatrix}\lambda &1&0&\cdots &0\\0&\lambda &1&\cdots &0\\\vdots &\vdots &\ddots &\ddots &\vdots \\0&0&0&\lambda &1\\0&0&0&0&\lambda \end{bmatrix}}.}$$