42 lines
910 B
Markdown
42 lines
910 B
Markdown
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$$
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\left(\begin{array}{c}
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\hat{F}_{1,i,j}\\ \hat{F}_{2,i,j} \\ \vdots \\ \hat{F}_{C-1,i,j} \\ \hat{F}_{C,i,j}
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\end{array}\right)
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=
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\begin{pmatrix}
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\frac{\gamma_1}{\sqrt{\hat{\sigma}^2_1}+\epsilon} & 0 & \cdots & &0
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\\
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0 && \frac{\gamma_2}{\sqrt{\hat{\sigma}^2_2}+\epsilon} & & & &
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\\
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\vdots && \ddots && \vdots
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\\
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&&& \frac{\gamma_{C-1}}{\sqrt{\hat{\sigma}^2_{C-1}+\epsilon}} & 0
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\\
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0 && \cdots &0 & \frac{\gamma_C}{\sqrt{\hat{\sigma}^2_{C}+\epsilon}}
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\end{pmatrix}
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\cdot
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\begin{pmatrix}
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F_{1,i,j}
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\\
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F_{2,i,j}
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\\
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\vdots
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\\
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F_{C-1,i,j}
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\\
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F_{C,i,j}
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\end{pmatrix}
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+
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\begin{pmatrix}
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\beta_1-\gamma_1\frac{\hat{\mu}_1}{\sqrt{\hat{\sigma}^2_1+\epsilon}}
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\\
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\beta_2-\gamma_2\frac{\hat{\mu}_2}{\sqrt{\hat{\sigma}^2_2+\epsilon}}
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\\
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\vdots
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\\
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\beta_{C-1}-\gamma_{C-1}\frac{\hat{\mu}_{C-1}}{\sqrt{\hat{\sigma}^2_{C-1}+\epsilon}}
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\\
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\beta_C-\gamma_C\frac{\hat{\mu}_C}{\sqrt{\hat{\sigma}^2_C+\epsilon}}
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\end{pmatrix}
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$$
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