# Is there a name for a general upper triangular hollow matrix?

A hollow matrix is one with zero diagonal elements (according to this web page)

Q1: Is there a name for an upper (or lower) triangular hollow matrix?

Q2: Alternatively how might such an object be written using conventional notation?

I took a look at this web page, and the only objects which come close are the Hessenberg matrices, but clearly not close enough !

I suppose I could say "... upper triangular matrix with zero diagonal elements," or "... upper triangular hollow matrix," but a more succinct expression would be nice...

• Strictly triangular matrix – Ofir Schnabel Aug 20 '15 at 8:40
• Of course ! :-) thanks. – Pixel Aug 20 '15 at 8:42
• No problem, the condition in the answer below. – Ofir Schnabel Aug 20 '15 at 8:47

These are strictly triangular matrices. A matrix $A=(a_{ij})\in M_n(F)$ is strictly (upper) triangular matrix if for $i\geq j$, $a_{ij}=0$.
• Hi Ofir, do you know if such matrices are denoted in a special way, e.g. an upper triangular matrix might be denoted $U$, whereas a strictly upper triangular matrix could be $U^*$, for example. Is there a standard notation or not? – Pixel Aug 20 '15 at 9:21
• Not in general. Notice that unlike the triangular case, the set of strictly upper triangular is not a sub algebra of $M_n(F)$, however it is a Lie sub algebra. Look here en.wikipedia.org/wiki/Triangular_matrix – Ofir Schnabel Aug 20 '15 at 9:26