随笔分类 - Math
摘要：May refer to this paper. Note that generally for an algebra we also know it should have representation and irrep.
阅读全文
摘要：Also refer to wikipedia link, we have:${\displaystyle \mathbf {J} _{\mathbf {f} ^{-1}}={\mathbf {J} _{\mathbf {f} }}^{-1}.}$
阅读全文
摘要：We consider $det(A\otimes B)$. Notice that $det(A\otimes B)=det(A\otimes II\otimes B)=det(A\otimes I)det(I\otimes B)$. Hence we have $det(A\otimes B)=
阅读全文
摘要：为什么SO(2)是一个Abel群? 可以从抽象的群元角度去理解:先转-60度再转30度和先转30度再转-60度是一样的；也可以从矩阵的角度去理解:\(\left( \begin{matrix} \cos\mathrm{(}\theta )& -\sin\mathrm{(}\theta )\\ \si
阅读全文
摘要：Proposition (The orthogonal complement of a column space). Let A be a matrix and let $W=\operatorname{Col}(A)$. Then $$ W^{\perp}=\operatorname{Nul}\l
阅读全文
摘要：Notation1 We use the convention that \(\Omega(x)\) means a function that is asymptotically \(\geq c_{1} x\) for a constant \(c_{1}>0, O(x)\) means \(\
阅读全文
摘要：$|1 − e^{i\theta}| ≥ 2|\theta|/\pi$ whenever $−\pi ≤ \theta ≤ \pi$ $-log x\ge (1-x)/ln2$ where $log$ has base $2$. $\left(\begin{array}{cccc} \Pi_{1}
阅读全文
摘要：Useful linkes: https://www.rampfesthudson.com/does-law-of-large-numbers-imply-central-limit-theorem/ https://en.wikipedia.org/wiki/Central_limit_theor
阅读全文
摘要：If we use sample mean: \(\frac{\sum_i{\left( X_i-\bar{X} \right)}^2}{n}\), then we should use sample variance:\(\frac{\sum_i{\left( X_i-\bar{X} \right
阅读全文
摘要：Refer links
阅读全文
摘要：Suppose \(p(x)\) is a polynomial of degree \(\leq n\) which is bounded in \([-1,+1]\) for \(x \in[-1,+1]\). What is the largest \(p^{\prime}(0)\) can
阅读全文
摘要：Norm Norm for vectors \[ \begin{aligned} &\|x\| \geq 0 \\ &\|x\|=0 \text { if and only if } x=0 \\ &\|c x\|=|c|\|x\| \\ &\|x+y\| \leq\|x\|+\|y\| \end{
阅读全文
浙公网安备 33010602011771号