SciTech-Mathmatics-RealAnalysis: Cantor-Schröder-Bernstein Theorem

【SciTech-Mathmatics-RealAnalysis: Cantor-Schröder-Bernstein Theorem】的更多相关文章

译注(2): How to Write a 21st Century Proof

原文:Computer Scientist Tells Mathematicians How To Write Proofs 对比一下下面两个证明哪个更好? 版本一: "A square and 10 roots are equal to 39 units. The question therefore in this type of equation is about as follows: what is the square which combined with ten of its r…

Parseval's theorem 帕塞瓦尔定理

Source: wiki: Parseval's theorem As for signal processing, the power within certain frequency band = the sum of (power spectrum at all frequencies within the frequency band)^2.…

利用Cayley-Hamilton theorem 优化矩阵线性递推

平时有关线性递推的题,很多都可以利用矩阵乘法来解决. 时间复杂度一般是O(K3logn)因此对矩阵的规模限制比较大. 下面介绍一种利用利用Cayley-Hamilton theorem加速矩阵乘法的方法. Cayley-Hamilton theorem: 记矩阵A的特征多项式为f(x). 则有f(A)=0. 证明可以看维基百科 https://en.wikipedia.org/wiki/Cayley–Hamilton_theorem#A_direct_algebraic_proof 另外我在高…

Kernel Methods (6) The Representer Theorem

The Representer Theorem, 表示定理. 给定: 非空样本空间: $\chi$ $m$个样本:$\{(x_1, y_1), \dots, (x_m, y_m)\}, x_i in \chi, y_i \in R$ 非负的损失函数: $J:(\chi \times R^2)^m \to R^+$. 这个符号表示初看挺别扭的, 从wikipedia上抄来的. 含义是$J$有$m \times 3$个参数, 3代表: 样本$x_i$ (一个\(\chi\…

cantor三分集

值得一提的是,第一次听说cantor三分集是在数字电路课上,然而数电是我最不喜欢的课程之一...... 分形大都具有自相似.自仿射性质,所以cantor三分集用递归再合适不过了,本来不想用matlab的,毕竟以后不会靠这东西.但是考虑到其方便的绘图功能还是用了.matlab写递归还是头一遭,心慌慌,不过试了一下发现和其他语言基本没差别! 源码 function cantor(Ax, Ay, Bx, By) precision = 0.001; if Bx-Ax < precision plot(…

加州大学伯克利分校Stat2.2x Probability 概率初步学习笔记: Section 4 The Central Limit Theorem

Stat2.2x Probability(概率)课程由加州大学伯克利分校(University of California, Berkeley)于2014年在edX平台讲授. PDF笔记下载(Academia.edu) Summary Standard Error The standard error of a random variable $X$ is defined by $$SE(X)=\sqrt{E((X-E(X))^2)}$$ $SE$ measures the rough size…