Alternative Equation Formats

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MathML

\begin{array}{rcl} \hat{β} & = & S_{11}^{- 1 / 2} [v_{1}, \dots, v_{r}] \\ \hat{α} & = & S_{01} \hat{β} ({\hat{β}}^{'} S_{11} \hat{β})^{- 1} \\ \hat{Π} & = & \hat{α} {\hat{β}}^{'} \\ {\hat{Ψ}}^{'} & = & (Z_{2}^{'} Z_{2})^{- 1} Z_{2}^{'} (Z_{0} - Z_{1} {\hat{Π}}^{'}) \\ \hat{Σ} & = & (Z_{0} - Z_{2} {\hat{Ψ}}^{'} - Z_{1} {\hat{Π}}^{'})^{'} (Z_{0} - Z_{2} {\hat{Ψ}}^{'} - Z_{1} {\hat{Π}}^{'}) / T \end{array}

Math Rendered as SVG

Math as LaTeX Source

\begin{eqnarray*} \hat{\bbeta } & =& S_{11}^{-1/2} [v_1,\ldots ,v_ r] \\ \hat{\balpha } & =& S_{01}\hat{\bbeta }(\hat{\bbeta }' S_{11}\hat{\bbeta })^{-1} \\ \hat\Pi & =& \hat{\balpha } \hat{\bbeta }' \\ \hat\Psi ' & =& (Z_{2}'Z_{2})^{-1} Z_{2}'(Z_{0} - Z_{1} \hat\Pi ') \\ \hat\Sigma & =& (Z_{0} - Z_{2} \hat\Psi ' - Z_{1} \hat\Pi ')' (Z_{0} - Z_{2} \hat\Psi ' - Z_{1} \hat\Pi ')/T \end{eqnarray*}