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...

  • 2
    $\begingroup$ Strictly triangular matrix $\endgroup$ – Ofir Schnabel Aug 20 '15 at 8:40
  • $\begingroup$ Of course ! :-) thanks. $\endgroup$ – Pixel Aug 20 '15 at 8:42
  • $\begingroup$ No problem, the condition in the answer below. $\endgroup$ – 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 $i\geq j$, $a_{ij}=0$.

  • $\begingroup$ 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? $\endgroup$ – Pixel Aug 20 '15 at 9:21
  • $\begingroup$ 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 $\endgroup$ – Ofir Schnabel Aug 20 '15 at 9:26

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