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feat: trans 2 main pattern
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@@ -25,19 +25,19 @@ Graphic notes on Gilbert Strang's "Linear Algebra for Everyone"
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我尝试为 Gilbert Strang 在书籍 “Linear Algebra for Everyone” 中介绍的矩阵的重要概念进行可视化图释, 以促进从矩阵分解的角度对向量、矩阵计算和算法的理解.
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它们包括矩阵分解 (Column-Row, CR)、高斯消去法 (Gaussian Elimination, LU)、格拉姆-施密特正交化 (Gram-Schmidt Orthogonalization, QR)、特征值和对角化 (Eigenvalues and Diagonalization, QΛQ')、和奇异值分解(Singular Value Decomposition, UΣV').
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也包括其他图形.
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## 特征值图
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- 可以在 PDF "[MapofEigenvalues](MapofEigenvalues-v1.1.pdf)"中查看
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## 矩阵世界
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- 可以在 PDF "[MatrixWorld](MatrixWorld.pdf)"中查看
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@@ -329,7 +329,7 @@ $A=CR, A=LU, A=QR, A=Q \Lambda Q\transp, A=U \Sigma V\transp$ 将一一说明.
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\end{itemize}
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所有一般的长矩阵$A$都有相同的行秩和列秩.
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这个分解是理解这一定力最直观的方法.
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这个分解是理解这一定理最直观的方法.
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$C$由$A$的线性无关列组成, $R$为$A$的行阶梯形矩阵 (消除了零行).
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$A=CR$将$A$化简为$r$的线性无关列$C$和线性无关行$R$的乘积.
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@@ -680,14 +680,14 @@ Ashley Fernandes 在排版时帮我美化了这篇论文, 使它更加一致和
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\href{https://anagileway.com/2021/10/01/map-of-eigenvalues/}{https://anagileway.com/2021/10/01/map-of-eigenvalues/}\\
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\begin{figure}[H]
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\centering
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\includegraphics[keepaspectratio, width=\linewidth]{MapofEigenvalues.eps}
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\includegraphics[keepaspectratio, width=\linewidth]{MapofEigenvalues-zh-CN.png}
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\caption{特征值图}
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\end{figure}
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\item Kenji Hiranabe(2020), \emph{Matrix World}, An Agile Way(blog),\\
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\href{https://anagileway.com/2020/09/29/matrix-world-in-linear-algebra-for-everyone/}{https://anagileway.com/2020/09/29/matrix-world-in-linear-algebra-for-everyone/}
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\begin{figure}[H]
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\centering
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\includegraphics[keepaspectratio, width=\linewidth]{MatrixWorld.eps}
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\includegraphics[keepaspectratio, width=\linewidth]{MatrixWorld-zh-CN.png}
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\caption{矩阵世界}
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\end{figure}
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\end{enumerate}
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