The singular value decomposition of a matrix %$A$% is defined as %BEGINLATEX{label="one" color="Green"}% \begin{displaymath} A = U \Sigma V^H \end{displaymath} %ENDLATEX%

where %$U$% and %$V$% are both matrices with orthonormal columns, %$\{\cdot\}^H$% indicates a complex-conjugate transpose, and %$\Sigma$% is a diagonal matrix with singular values %\[ \sigma_1 > \sigma_2 > \cdots > \sigma_n \geq 0 \]% along the main diagonal. Eq. %REFLATEX{one}% is just one of the many matrix decompositions that exists for matrix %$A$%.

%beginlatex{label="two"}% \begin{equation} A = U \Sigma V^H \end{equation} %endlatex%

where Equ. %reflatex{two}%

%$R_{av}\approx R_{s}=R_{L}/4$% and hence %$k/R^{2}_{L} \approx k/16R^2_{av}$%

-- JohnBoggs - 16 Feb 2008