\(
T(f^{-1})( (y_1, \ldots, y_{m}),
\begin{pmatrix}
\eta_1 \\
\vdots \\
\eta_{m}
\end{pmatrix}) \\ = \\
(f^{-1}(y_1, \ldots, y_{m}), \\
\begin{pmatrix}
\frac{\partial f_1}{\partial x_1}(f^{-1}(y_1, \ldots, y_{m})) & \ldots & \frac{\partial f_1}{\partial x_{\ell}}(f^{-1}(y_1, \ldots, y_{m})) \\
\vdots & \ddots & \vdots \\
\frac{\partial f_{m}}{\partial x_1}(f^{-1}(y_1, \ldots, y_{m})) & \ldots & \frac{\partial f_{m}}{\partial x_{\ell}}(f^{-1}(y_1, \ldots, y_{m})) \\
\end{pmatrix}^{\triangleleft}
\cdot \\
\begin{pmatrix}
\eta_1 \\
\vdots \\
\eta_{m}
\end{pmatrix}
)
\)
表示されているとこだけ切り出す。↓
\(
\begin{pmatrix}
\frac{\partial f_1}{\partial x_1}(f^{-1}(y_1, \ldots, y_{m})) & \ldots & \frac{\partial f_1}{\partial x_{\ell}}(f^{-1}(y_1, \ldots, y_{m})) \\
\vdots & \ddots & \vdots \\
\frac{\partial f_{m}}{\partial x_1}(f^{-1}(y_1, \ldots, y_{m})) & \ldots & \frac{\partial f_{m}}{\partial x_{\ell}}(f^{-1}(y_1, \ldots, y_{m})) \\
\end{pmatrix}^{\triangleleft}
\)
ちょいと追加。↓
\(
f^{-1}(y_1, \ldots, y_{m}), \\
\begin{pmatrix}
\frac{\partial f_1}{\partial x_1}(f^{-1}(y_1, \ldots, y_{m})) & \ldots & \frac{\partial f_1}{\partial x_{\ell}}(f^{-1}(y_1, \ldots, y_{m})) \\
\vdots & \ddots & \vdots \\
\frac{\partial f_{m}}{\partial x_1}(f^{-1}(y_1, \ldots, y_{m})) & \ldots & \frac{\partial f_{m}}{\partial x_{\ell}}(f^{-1}(y_1, \ldots, y_{m})) \\
\end{pmatrix}^{\triangleleft}
\)
丸括弧追加。↓
\(
(
f^{-1}(y_1, \ldots, y_{m}), \\
\begin{pmatrix}
\frac{\partial f_1}{\partial x_1}(f^{-1}(y_1, \ldots, y_{m})) & \ldots & \frac{\partial f_1}{\partial x_{\ell}}(f^{-1}(y_1, \ldots, y_{m})) \\
\vdots & \ddots & \vdots \\
\frac{\partial f_{m}}{\partial x_1}(f^{-1}(y_1, \ldots, y_{m})) & \ldots & \frac{\partial f_{m}}{\partial x_{\ell}}(f^{-1}(y_1, \ldots, y_{m})) \\
\end{pmatrix}^{\triangleleft}
)
\)
もう少し追加↓
\(
(
f^{-1}(y_1, \ldots, y_{m}), \\
\begin{pmatrix}
\frac{\partial f_1}{\partial x_1}(f^{-1}(y_1, \ldots, y_{m})) & \ldots & \frac{\partial f_1}{\partial x_{\ell}}(f^{-1}(y_1, \ldots, y_{m})) \\
\vdots & \ddots & \vdots \\
\frac{\partial f_{m}}{\partial x_1}(f^{-1}(y_1, \ldots, y_{m})) & \ldots & \frac{\partial f_{m}}{\partial x_{\ell}}(f^{-1}(y_1, \ldots, y_{m})) \\
\end{pmatrix}^{\triangleleft}
\cdot \\
\begin{pmatrix}
\eta_1 \\
\vdots \\
\eta_{m}
\end{pmatrix}
)
\)
ダメになった。行列削除。
\(
(
f^{-1}(y_1, \ldots, y_{m}), \\
\begin{pmatrix}
\frac{\partial f_1}{\partial x_1}(f^{-1}(y_1, \ldots, y_{m})) & \ldots & \frac{\partial f_1}{\partial x_{\ell}}(f^{-1}(y_1, \ldots, y_{m})) \\
\vdots & \ddots & \vdots \\
\frac{\partial f_{m}}{\partial x_1}(f^{-1}(y_1, \ldots, y_{m})) & \ldots & \frac{\partial f_{m}}{\partial x_{\ell}}(f^{-1}(y_1, \ldots, y_{m})) \\
\end{pmatrix}^{\triangleleft}
\cdot \\
)
\)
削除した行列がヤバイのか？
\(
\begin{pmatrix}
\eta_1 \\
\vdots \\
\eta_{m}
\end{pmatrix}
\)
そうらしい。横1行ならどうだ？↓
\( \begin{pmatrix} \eta_1 \\ \vdots \\ \eta_{m} \end{pmatrix} \)
ダメか、中身削ってみる。
\( \begin{pmatrix} \eta_1 \end{pmatrix} \)
これでは？
\( \begin{pmatrix} 1 \end{pmatrix} \)
エータがダメなのか。
\( \begin{pmatrix} \xi_1 \end{pmatrix} \)
エータをローにしたらどうだ。
\(
T(f^{-1})( (y_1, \ldots, y_{m}),
\begin{pmatrix}
\rho_1 \\
\vdots \\
\rho_{m}
\end{pmatrix}) \\ = \\
(f^{-1}(y_1, \ldots, y_{m}), \\
\begin{pmatrix}
\frac{\partial f_1}{\partial x_1}(f^{-1}(y_1, \ldots, y_{m})) & \ldots & \frac{\partial f_1}{\partial x_{\ell}}(f^{-1}(y_1, \ldots, y_{m})) \\
\vdots & \ddots & \vdots \\
\frac{\partial f_{m}}{\partial x_1}(f^{-1}(y_1, \ldots, y_{m})) & \ldots & \frac{\partial f_{m}}{\partial x_{\ell}}(f^{-1}(y_1, \ldots, y_{m})) \\
\end{pmatrix}^{\triangleleft}
\cdot \\
\begin{pmatrix}
\rho_1 \\
\vdots \\
\rho_{m}
\end{pmatrix}
)
\)
なるほど、エータ（η）が原因だ。が、なぜ？ なぜにエータがダメ？ しかも環境依存でダメになる。HTTPとHTTPSか？？
