Examples

The packed storage scheme is illustrated by the following example, where $n = 4$:

$$A = \left( \begin{array}{rrrr} a_{11} & a_{12} & a_{13} & a... ...{34} \\ a_{41} & a_{42} & a_{43} & a_{44} \end{array} \right)$$

where $a_{ij} = a_{ji} \;\; \mbox{for} \;\; i,j = 1, \cdots, 4.$

Packed storage of the upper triangle of $A$:

$$\begin{array}{c} {\bf AP} \\ \begin{array}{\vert rrrrrrrr... ...} & a_{24} & a_{34} & a_{44} \\ \hline \end{array} \end{array}$$

Packed storage of the lower triangle of $A$:

$$\begin{array}{c} {\bf AP} \\ \begin{array}{\vert rrrrrrrr... ...} & a_{33} & a_{43} & a_{44} \\ \hline \end{array} \end{array}$$