Alternative Equation Formats

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MathML

\begin{array}{rcl} r_{t} & = & H_{t}^{\frac{1}{2}} ϵ_{t} \\ H_{t} & = & C + A_{1}^{'} r_{t - 1} r_{t - 1}^{'} A_{1} + G_{1}^{'} H_{t - 1} G_{1} \\ = & [\begin{array}{cc} c_{11} & c_{12} \\ c_{12} & c_{22} \end{array}] + {[\begin{array}{cc} a_{11, 1} & a_{12, 1} \\ a_{21, 1} & a_{22, 1} \end{array}]}^{'} [\begin{matrix} r_{1, t - 1} \\ r_{2, t - 1} \end{matrix}] {[\begin{matrix} r_{1, t - 1} \\ r_{2, t - 1} \end{matrix}]}^{'} [\begin{array}{cc} a_{11, 1} & a_{12, 1} \\ a_{21, 1} & a_{22, 1} \end{array}] \\ + & {[\begin{array}{cc} g_{11, 1} & g_{12, 1} \\ g_{21, 1} & g_{22, 1} \end{array}]}^{'} [\begin{array}{cc} h_{11, t - 1} & h_{12, t - 1} \\ h_{12, t - 1} & h_{22, t - 1} \end{array}] [\begin{array}{cc} g_{11, 1} & g_{12, 1} \\ g_{21, 1} & g_{22, 1} \end{array}] \end{array}

Math Rendered as SVG

Math as LaTeX Source

\begin{eqnarray*} r_ t & = & H_ t ^{\frac{1}{2}} \bepsilon _ t \\ H_ t & = & C + A_1' r_{t-1} r_{t-1}' A_1 + G_1' H_{t-1} G_1 \\ & = & \left[ \begin{array}{cc} c_{11} & c_{12} \\ c_{12} & c_{22} \end{array} \right] + \left[ \begin{array}{cc} a_{11,1} & a_{12,1} \\ a_{21,1} & a_{22,1} \end{array} \right]' \left[ \begin{array}{c} r_{1,t-1} \\ r_{2,t-1} \end{array} \right] \left[ \begin{array}{c} r_{1,t-1} \\ r_{2,t-1} \end{array} \right]' \left[ \begin{array}{cc} a_{11,1} & a_{12,1} \\ a_{21,1} & a_{22,1} \end{array} \right] \\ & + & \left[ \begin{array}{cc} g_{11,1} & g_{12,1} \\ g_{21,1} & g_{22,1} \end{array} \right]' \left[ \begin{array}{cc} h_{11,t-1} & h_{12,t-1} \\ h_{12,t-1} & h_{22,t-1} \end{array} \right] \left[ \begin{array}{cc} g_{11,1} & g_{12,1} \\ g_{21,1} & g_{22,1} \end{array} \right] \end{eqnarray*}