vault backup: 2025-04-10 14:02:57

.obsidian/plugins/obsidian-enhancing-export-main/tests/markdowns/math-block-01.md

@@ -0,0 +1,51 @@
+$$
+\left(\begin{array}{c}
+\hat{F}_{1,i,j}\\ \hat{F}_{2,i,j} \\ \vdots \\ \hat{F}_{C-1,i,j} \\ \hat{F}_{C,i,j}
+\end{array}\right)
+
+=
+
+\begin{pmatrix}
+\frac{\gamma_1}{\sqrt{\hat{\sigma}^2_1}+\epsilon} & 0 & \cdots & &0
+\\
+0 && \frac{\gamma_2}{\sqrt{\hat{\sigma}^2_2}+\epsilon} & & & &
+\\
+\vdots && \ddots && \vdots
+\\
+&&& \frac{\gamma_{C-1}}{\sqrt{\hat{\sigma}^2_{C-1}+\epsilon}} & 0
+\\
+0 && \cdots &0 & \frac{\gamma_C}{\sqrt{\hat{\sigma}^2_{C}+\epsilon}}
+
+\end{pmatrix}
+
+
+\cdot
+
+\begin{pmatrix}
+F_{1,i,j}
+\\
+F_{2,i,j}
+\\
+\vdots
+\\
+F_{C-1,i,j}
+\\
+
+F_{C,i,j}
+\end{pmatrix}
+
++
+
+\begin{pmatrix}
+\beta_1-\gamma_1\frac{\hat{\mu}_1}{\sqrt{\hat{\sigma}^2_1+\epsilon}}
+\\
+\beta_2-\gamma_2\frac{\hat{\mu}_2}{\sqrt{\hat{\sigma}^2_2+\epsilon}}
+\\
+\vdots
+\\
+\beta_{C-1}-\gamma_{C-1}\frac{\hat{\mu}_{C-1}}{\sqrt{\hat{\sigma}^2_{C-1}+\epsilon}}
+\\
+\beta_C-\gamma_C\frac{\hat{\mu}_C}{\sqrt{\hat{\sigma}^2_C+\epsilon}}
+
+\end{pmatrix} 
+$$