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Trance-0
2025-12-01 15:40:03 -06:00
parent 12ae242e90
commit 55decba076
2 changed files with 3 additions and 2 deletions
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content/CSE5313/CSE5313_L25.md
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@@ -165,9 +165,10 @@ G=\begin{bmatrix}
\ell_1(\alpha_1) & \ell_1(\alpha_2) & \cdots & \ell_1(\alpha_P) \\ \ell_1(\alpha_1) & \ell_1(\alpha_2) & \cdots & \ell_1(\alpha_P) \\
\ell_2(\alpha_1) & \ell_2(\alpha_2) & \cdots & \ell_2(\alpha_P) \\ \ell_2(\alpha_1) & \ell_2(\alpha_2) & \cdots & \ell_2(\alpha_P) \\
\vdots & \vdots & \ddots & \vdots \\ \vdots & \vdots & \ddots & \vdots \\
\ell_K)(\alpha_1) & \ell_K(\alpha_2) & \cdots & \ell_K(\alpha_P) \\ \ell_K(\alpha_1) & \ell_K(\alpha_2) & \cdots & \ell_K(\alpha_P) \\
\vdots & \vdots & \ddots & \vdots \\ \vdots & \vdots & \ddots & \vdots \\
\ell_{K+T}(\alpha_1) & \ell_{K+T}(\alpha_2) & \cdots & \ell_{K+T}(\alpha_P) \ell_{K+T}(\alpha_1) & \ell_{K+T}(\alpha_2) & \cdots & \ell_{K+T}(\alpha_P)
\end{bmatrix}
$$ $$
For analysis, we denote $G=\begin{bmatrix}G^{top}\\G^{bot}\end{bmatrix}$, where $G^{top}\in \mathbb{F}^{K\times P}$ and $G^{bot}\in \mathbb{F}^{T\times P}$. For analysis, we denote $G=\begin{bmatrix}G^{top}\\G^{bot}\end{bmatrix}$, where $G^{top}\in \mathbb{F}^{K\times P}$ and $G^{bot}\in \mathbb{F}^{T\times P}$.

2
content/Math4201/Math4201_L37.md
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@@ -77,4 +77,4 @@ Choose $p,q\in \mathbb{Q}$ such that $c<p<f(x_0)<q<d$.
By our construction, $x_0\in \overline{U_q}-U_p$, and $f(\overline{U_q}-U_p)\subseteq [p,q]\subset (c,d)$. By our construction, $x_0\in \overline{U_q}-U_p$, and $f(\overline{U_q}-U_p)\subseteq [p,q]\subset (c,d)$.
</details> </details>