C-Matrix

Any Symmetric Matrix ( ${\hbox{\sf A}}^{\rm T} = {\hbox{\sf A}}$ ) or Skew Symmetric Matrix ( ${\hbox{\sf A}}^{\rm T}=-{\hbox{\sf A}}$ ) ${\hbox{\sf C}}_n$ with diagonal elements 0 and others $\pm 1$ satisfying

$\begin{displaymath} {\hbox{\sf C}}{\hbox{\sf C}}^{\rm T} = (n-1){\hbox{\sf I}}, \end{displaymath}$

where I is the Identity Matrix, is known as a

-matrix (Ball and Coxeter 1987). Examples include

$\displaystyle {\hbox{\sf C}}_4$	$\textstyle =$	$\displaystyle \left[\begin{array}{cccc}0 & + & + & + \\ - & 0 & - & + \\ - & + & 0 & - \\ - & - & + & 0\end{array}\right]$
$\displaystyle {\hbox{\sf C}}_6$	$\textstyle =$	$\displaystyle \left[\begin{array}{ccccccccccccccccccccccccccccccc}0 & + & + & +... ...& - & + & 0 & + \nonumber\\ + & + & - & - & + & 0 \end{array}\right].\nonumber$

References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 308-309, 1987.