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Numerical Linear Algebra Homework Week 3 Class 1
Numerical Linear Algebra T1 <div class="cbox" 2.18 证明对于可逆矩阵 有 . </div <div class="pbox" $ A \in \mathbb{R}^{n \times n} v Av+\Delta Av=0 \|\Delta Av\| 2=\|Av\| 2\ge \sigma 1 \max...
Number Theory Homework 2
Number Theory Homework 2 T1 <div class="cbox" 1. 证明: 当 时, 在辗转相除法中, . </div <div class="pbox" 这为啥是辗转相除...这不是不同带余除法吗... $ a = bq 1 + r 1, b/2 \le r 1 < b/2 q 1 = \left[\frac{2a}{b}\...
Math Analysis 3 Homework 2
Math Analysis 3 Homework 2 T1 <div class="cbox" Problem 1. 设 , 当 时 , 当 时 , 而对一切 , . 1. 求 的傅里叶系数; 2. 证明: $ \delta \to 0 \delta = \frac{\pi}{2} f x=0 b n=0 f S n(f,x)\to \dfrac{f(x^...
Complex Analysis Homework 3
Complex Analysis Homework 3 T1 <div class="cbox" 1. (复可微性的定义) 复可微性的定义是否可弱化呢? 考虑函数 $ \ell \lim {\ell \ni z \to 0} (f(z) f(0))/z = 0 f 0 x = y^2 0 f \Omega g(z) = \overline{f(\overl...
Algebraic Topology Homework 1
Algebraic Topology Homework 1 T1 <div class="cbox" 5. Show that for a space , the following three conditions are equivalent: (a) Every map is homotopic to a constant map, with ima...
Complex Analysis Homework 2
Complex Analysis Homework 2 Class 1 T1 <div class="cbox" 证明集合 是闭集的充分必要条件是 包含其所有的极限点. </div <div class='pbox' 反证.假设存在一个 内点列 其极限点 不在 内,则 是开集,故存在 ,但 收敛于 要求 ,则取 推得 与 是 内的点列矛盾.故得证. </d...
Probability Homework 2
Probability Homework 2 Class 1 T1 <div class="cbox" 32. 投掷两枚均匀的骰子直到出现点数之和为 5 或者 7, 求和为 5 先出现的概率. 提示: 设事件 为第 次投掷的点数之和为 5 且在此之前没有出现点数之和为 5 或 7 的情况, 计算 并证明 为所求概率. </div <div class="p...
Numerical Linear Algebra Homework Week 2 Class 1
Numerical Linear Algebra Homework Week 2 Class 1 T1 <div class="cbox" 1.11 举例说明通过向量 范数定义的矩阵范数 $ \|AB\| {\max} \leqslant \|A\| {\max} \|B\| {\max} \mathbb{R}^{m\times n} \|\cdot\|...
Numerical Linear Algebra Homework Week 2 Class 2
Numerical Linear Algebra Homework Week 2 Class 2 T1 <div class="cbox" 2.3 设 为可逆矩阵, 思考如何用 Gauss 消去或者 LU 分解计算 的逆, 并且进行算法实现. 读者可以通过与 MATLAB/Octave/北太天元等自带函数 “ ” 或者 进行比较验证算法的正确性. </di...
Number Theory Homework 1
Number Theory Homework 1 T1 <div class="cbox" 1. 用辗转相除法求 并求一组 使得 . </div <div class="pbox" $ (210, 330, 1155) x, y, z \in \mathbb{Z} (210, 330, 1155) = 210x 330y + 1155z (210, 330...
Restore Gemini on Chrome
Restore Gemini on Chrome You don't need to edit some "Local State" files. Just run And it'll be displayed again.