# Name of a specific upper-triangular matrix

What is the name (if any does exist) of an upper-triangular matrix whose elements on each diagonal are equal? Also, are there any properties associated with this matrix or not?

• They are a constant multiple of unipotent matrices, which are matrices $A$ such that $A-I$ is nilpotent, i.e. $(A-I)^{m} = O$ for some $m>0$. – Seewoo Lee May 26 at 0:00
It is notable that every such matrix can be written as a polynomial of the matrix $$M = \pmatrix{0&1&0\\0&0&1&0\\&&\ddots&\ddots&\\ &&&&1\\ &&&&0}$$ and that any two such matrices commute.