Basic Variance $Var(X)=E[X^2]-E[X]^2$ Advance PMF v.s PDF v.s CDF PMF (Probability Mass function) A PMF is a mathematical function that gives the probability that a discrete random variable is exactly equal to a specific value. It is used in statistics to describe the distribution of discrete random variables. $p(x) = P(X=x)$, $p(x)$ is PMF

Topics flowchart LR LG(Linear Geometry)-->LS(Linear Space)-->LF(Linaer Function) Linear GeometrySystems of Linear Equations Linear Space Vector Spaces Linaer Function

中山大學資訊工程學系全英班 我的第一場面試，當天頗熱，前面有兩個人沒報到，中間我覺得我算回答的2266的，不過教授人都還不錯，很和善。 不同於一般班，我們是個別面試，分為數理面向及英文面向各兩位教授，沒有自我介紹（人家準備了的說…）。 然後對其他考生的觀察的部分，女生大部份穿的像辦公室OL，男生從全套西裝到稍微不那麼正式的短袖襯衫我都有看到，然後我還在路上（不確定哪個系的）穿格子襯衫+牛仔褲。 數理面向 以抽籤選題，給五分鐘解題，解完題後教授會問你解題思路及為什麼選擇這個解法，題目及問答皆為英文。 題目 求以下式之三根（有給選項）

Simple operations Matrix addition I think most of us learnt it in high school, so let's just give an example. :::info what is result of $\left[ {\begin{array}{cc} 1 & 2 & 3\ 4 & 5 & 6 \ \end{array} } \right]+ \left[ {\begin{array}{cc} 1 & 3 & 5\

Linear Algebra - Introduction Systems of Linear Equations Linear Algebra - Vector Linear Algebra - Vector and Set of Vectors Linear Algebra - Systems of Linear Equations Vector Spaces Linear Algebra - Vector Space Linear Algebra - Subspace

# Linear Algebra - Matrix Inverse

https://hackmd.io/@benny-liu/SkuD7zJBJx 幸運地，抑或者是不幸地，我這學期暈船了。 註: 暈船，指快速喜歡上一個人，或對某人產生強烈迷戀，並且通常是指不可能有結果的愛情。 這邊就不提狗血戀愛腦的部分了，在暈船以來差不多一個月的時間，剛好會遇到一次月經，這時候我發現一件非常有趣的現象，在暈船時，我的月經血量會比平常多更多，而更奇妙的事，在血量增多的同時，我的經痛卻減少了。這時我想到，會不會是暈船時，大腦中的某些激素造成了這一現象。 本筆記分三段: 「暈船時的大腦狀態」、「是甚麼影響我的月經呢?」，最後是「我的結論」。

PART (II) - 03 Other parts in this series $\rightarrow$ Data Structure - Syllabus Sorting Algorithms A Sorting Algorithm is used to rearrange a given array or list of elements according to a comparison operator on the elements. The comparison operator is used to decide the new order of elements in the respective data structure. Sorting Terminology In-place Sorting: An in-place sorting algorithm uses constant space for producing the output (modifies the given array only) or copying elements to a temporary storage. Examples: Selection Sort, Bubble Sort Insertion Sort and Heap Sort. Internal Sorting: Internal Sorting is when all the data is placed in the main memory or internal memory. In internal sorting, the problem cannot take input beyond its size. Example: heap sort, bubble sort, selection sort, quick sort, shell sort, insertion sort.

https://hackmd.io/@benny-liu/Syi9ifIZkl Week06 運動與知覺 射箭(複合弓)很困難嗎? flowchart LR 1([內在動機])-->2([計畫])-->3([訊息傳遞])-->4([精細控制])-->5([動作結果]) 內在動機 我要把箭射到黃心。 計畫

可以使用Ctrl+F直接尋找題目 SELECT 01. 顯示所有圖書館內書籍的資料(資料表Allbooks)。 SELECT * FROM allbooks; 02. 在圖書館內的書籍中，請列出分類為 “電腦” 的書籍。 SELECT allbooks.* FROM allbooks, category WHERE cate=category.cid AND category.catename="電腦";

Definition for all vectors $\vec{u}$, $\vec{v}$, $\vec{w} \in V$, and $r$,$s\in\mathbb{R}$, if rule explain rule explain $\vec{v}+\vec{w}\in V$ close under addition

Definition For all vector space,a subspace is a subset that is itself a vector space, under the inheriate operation. Lemma If $W$ is a vector space, $V\subseteq W$, $\forall$ $\vec{v},\vec{w}\in V, r\in V$ $\vec{0}\in V$ $\vec{v}+\vec{w}\in V$ $r\vec{v}\in V$

We gonna expalin Linear Equations and its extentions, such as ker(),row(), pivot, leading variables & free variables Linear Equations In mathematics, a linear equation is an equation that may be put in the form $c_1x_1+c_2x_2...c_nx_n=a$, and $c_1,c_2...c_n$ are the coefficients, which are often real numbers. When there are a lot of equetions to slove we simply list them down. $$\begin{cases} c_{11}x_1+c_{12}x_2...c_{1n}x_n=a_1 \ c_{21}x_1+c_{22}x_2...c_{2n}x_n=a_2 \ \vdots\

Basis Definition A basis for vector space is a sequence of vector that is linearly independent and that spans the space. Examples basis of $\mathbb{R}^n={\left[ {\begin{array}{} 1\0\0\\vdots\0\end{array} } \right],\left[ {\begin{array}{} 0\1\0\\vdots\0\end{array} } \right],...,\left[ {\begin{array}{} 0\0\0\\vdots\1\end{array} } \right]}$ basis of $V={\left[ {\begin{array}{} x\y\z\end{array} } \right]\mid x+y+z=0}$ is ${\left[ {\begin{array}{} -1\1\0\end{array} } \right],\left[ {\begin{array}{} -1\0\1\end{array} } \right]}$ Dimension Definition

Definition In any vector space, a set of vector is 'linear independent' if none of its element is a linear combination of others from the set. Otherwise, it is it is linear dependent. Lemma If a linear combination of an independent set of vectors equals $\vec{0}$, then all coefficiant is 0. $$c_1u_1+c_2u_2+...+c_du_d=\vec{0}\rightarrow c_1=c_2=...=c_d=0$$ For a linear independent set ${u_1,u_2,...u_d}$ $$ker(\left[ {\begin{array}{} |&|&...&|\u_1 & u_2 & ... & u_d\|&|&...&| \end{array} } \right])=\vec{0}$$

Linear Combination Given a set of vectors S, $S={u_1,u_2,...,u_n }$, Linear combination of S is $$c_1u_1+c_2u_2+...+c_nu_n\text{ , such that }c_1,c_2,...,c_n\in\mathbb{R}$$ Span Span(S) is linear combiantion of S $$Span(S)={c_1u_1+c_2u_2+...+c_nu_n|c_1,c_2,...,c_n\in\mathbb{R}}$$ How to show vector is in a span or not? Let's just took some examples.

Vector :::info Some key points you should know in highschool. ::: How to calculate the length of a given vector? How to calculate the distance between two points?(Basically same as previous one) How to calculate the angle between two vectors using the law of cosine?law of cosine : $cos(C)=\cfrac{a^2+b^2-c^2}{2ab}$ How to calculate the angle between two vectors using the inner product?

CPE CPE心得 CPE49 UVa100 - The 3n + 1 problem UVa118 - Mutant Flatworld Explorers UVa272 - TEX Quotes UVa299 - Train Swapping UVa490 - Rotating Sentences UVa948 - Fibonaccimal Base

首戰 年級: 大二上 成績: 三題 抱怨: 瘋狂程設靠北難用，有時候不是你的問題，是編譯器問題。 可加強: 閱讀能力、基本刷題

Prblem link Review 無 Ans #include <iostream> using namespace std; int main(){ int a,b;