Alternative Equation Formats

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MathML

\begin{aligned} E ({\hat{u}}_{f}^{^{'}} P {\hat{u}}_{f}) & = (M - N - T - K + 1) σ_{e}^{2} \\ E ({\hat{u}}_{f}^{^{'}} P_{λ} {\hat{u}}_{f}) & = (T + k_{N} - k_{0}) σ_{e}^{2} + (T - δ_{N}) σ_{ν}^{2} + (M - δ_{T}) σ_{λ}^{2} \\ E ({\hat{u}}_{f}^{^{'}} P_{ν} {\hat{u}}_{f}) & = (N + k_{T} - k_{0}) σ_{e}^{2} + (M - δ_{N}) σ_{ν}^{2} + (N - δ_{T}) σ_{λ}^{2} \end{aligned}

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Math as LaTeX Source

\begin{align*} E\left(\hat{\mb{u}}_ f^{'} \mb{P} \hat{\mb{u}}_ f\right) & = (M - N - T - K + 1) \sigma ^2_ e \\ E\left(\hat{\mb{u}}_ f^{'} \mb{P}_\lambda \hat{\mb{u}}_ f\right) & = \left(T +k_ N- k_0\right)\sigma ^{2}_ e + (T- \delta _ N) \sigma ^2_\nu + (M- \delta _ T) \sigma ^2_\lambda \\ E\left(\hat{\mb{u}}_ f^{'} \mb{P}_\nu \hat{\mb{u}}_ f\right) & = \left(N +k_ T- k_0\right)\sigma ^2_ e + (M- \delta _ N) \sigma ^2_\nu + (N- \delta _ T) \sigma ^2_\lambda \end{align*}