feat: trans 2 main pattern

This commit is contained in:
kefangliu
2022-11-08 22:49:37 +08:00
parent fb9b01b9af
commit 0228178cdb
12 changed files with 6 additions and 6 deletions
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@@ -25,19 +25,19 @@ Graphic notes on Gilbert Strang's "Linear Algebra for Everyone"
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.
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').
![5种分解](5-Factorizations.png)
![5种分解](5-Factorizations-zh-CN.png)
也包括其他图形.
## 特征值图
![特征值图](MapofEigenvalues.png)
![特征值图](MapofEigenvalues-zh-CN.png)
- 可以在 PDF "[MapofEigenvalues](MapofEigenvalues-v1.1.pdf)"中查看
## 矩阵世界
![矩阵世界](MatrixWorld.png)
![矩阵世界](MatrixWorld-zh-CN.png)
- 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.
\end{itemize}
所有一般的长矩阵$A$都有相同的行秩和列秩.
这个分解是理解这一定最直观的方法.
这个分解是理解这一定最直观的方法.
$C$$A$的线性无关列组成, $R$$A$的行阶梯形矩阵 (消除了零行).
$A=CR$$A$化简为$r$的线性无关列$C$和线性无关行$R$的乘积.
@@ -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
\href{https://anagileway.com/2021/10/01/map-of-eigenvalues/}{https://anagileway.com/2021/10/01/map-of-eigenvalues/}\\
\begin{figure}[H]
\centering
\includegraphics[keepaspectratio, width=\linewidth]{MapofEigenvalues.eps}
\includegraphics[keepaspectratio, width=\linewidth]{MapofEigenvalues-zh-CN.png}
\caption{特征值图}
\end{figure}
\item Kenji Hiranabe(2020), \emph{Matrix World}, An Agile Way(blog),\\
\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/}
\begin{figure}[H]
\centering
\includegraphics[keepaspectratio, width=\linewidth]{MatrixWorld.eps}
\includegraphics[keepaspectratio, width=\linewidth]{MatrixWorld-zh-CN.png}
\caption{矩阵世界}
\end{figure}
\end{enumerate}
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