Alternative Equation Formats

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MathML

\begin{aligned} ρ & = Θ^{- 1} (σ μ (Z^{- 1} - V^{- 1}) e - Z^{- 1} Z_{a f f} S_{a f f} e + V^{- 1} V_{a f f} W_{a f f} e) \\ Δ t_{c} & = (A Θ^{- 1} A^{'})^{- 1} A ρ \\ Δ z_{c} & = Θ^{- 1} A^{'} Δ t_{c} - ρ \\ Δ v_{c} & = - Δ z_{c} \\ Δ w_{c} & = σ μ V^{- 1} e - V^{- 1} V_{a f f} W_{a f f} e - V^{- 1} W_{a f f} Δ v_{c} \\ Δ s_{c} & = σ μ Z^{- 1} e - Z^{- 1} Z_{a f f} S_{a f f} e - Z^{- 1} S_{a f f} Δ z_{c} \end{aligned}

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Math as LaTeX Source

\begin{align*} \brho & =\bTheta ^{-1} (\sigma \mu (\bZ ^{-1} - \bV ^{-1}) \mb{e} - \bZ ^{-1} \bZ _{\mathit{aff}} \bS _{\mathit{aff}} \mb{e} + \bV ^{-1} \bV _{\mathit{aff}} \bW _{\mathit{aff}} \mb{e}) \\ \bDelta t_ c & = (\bA \bTheta ^{-1} \bA ^{\prime })^{-1} \bA \brho \\ \bDelta z_ c & = \bTheta ^{-1} \bA ^{\prime } \bDelta t_ c - \brho \\ \bDelta v_ c & = -\bDelta z_ c \\ \bDelta w_ c & = \sigma \mu \bV ^{-1} \mb{e} - \bV ^{-1} \bV _{\mathit{aff}} \bW _{\mathit{aff}} \mb{e} - \bV ^{-1} \bW _{\mathit{aff}} \bDelta v_ c \\ \bDelta s_ c & = \sigma \mu \bZ ^{-1} \mb{e} - \bZ ^{-1} \bZ _{\mathit{aff}} \bS _{\mathit{aff}} \mb{e} - \bZ ^{-1} \bS _{\mathit{aff}} \bDelta z_ c \\ \end{align*}