%---------------------------Skew-----------------------------
\section{Skew}

First define normalized principal axes
\[
\begin{array}{lcl}
\hat X_1 &=& \frac {\vec X_1} {\normvec{X_1}}\\
\hat X_2 &=& \frac {\vec X_2} {\normvec{X_2}}.
\end{array}
\]

The skew is then
\[
q = | \hat X_1 \cdot \hat X_2 |.
\]
A geometric intepretation of the skew is that it measures the angle between the principal axes.
In fact, it is the absolute value of the cosine of the angle between the principal axes.

Note that if $\normvec{X_1}$ or $\normvec{X_2} < DBL\_MIN$, we set $q = 0$.

\quadmetrictable{skew}%
{$1$}%                                      Dimension
{$[0.5,1]$}%                                Acceptable range
{$[0,1]$}%                                  Normal range
{$[0,1]$}%                                  Full range
{$1$}%                                      Unit square
{Adapted from \cite{rob:87}}%               Citation
{v\_quad\_skew}%                            Verdict function name