Def of Linear transformation: Let and be vector spaces(over ). A function is called a linear transformation from into if for all and such that: &l...

Theorem: The and have the same dimension.(In spite of the size of ) Proof: Let be the RREF of Number of leading1's variables Def of ra...

Def of Row vector and column vector: For any m-by-n matrix , the vectors ,,, in that are formed from the rows of are called the row vectors of , and the...

Dimension(向量空間維度) Theorem(基底向量個數恆定): Let be a finite-dimensional vector space and let be a basis for , then <a>If a set in that has more than ...

basis(基底) Def of basis: If is any vector space and is a subset of , then is called a basis for if the following two conditions hold: <a> is l...

線性獨立 Def： If is a nonempty set of a vector space , then the vector equation has at least one solution, the trivial solution. If this is the only soluti...

向量空間子空間定義 A subset of a vector space $V is called a subspace of is is itself a vector space under the addition and scalar multiplication defined on . ...

向量空間定義 Def: Let be an arbitary nonempty set of object on which two operations called addition and scalar multiplication, are defined so that for each pa...

前言 之前討論的都是離散型的分布，意即隨機變數的取值是可數的。而本章討論取值不可數的連續情況。 連續隨機變數的機率密度函數和累積分布函數 類似於離散型隨機變數的機率質量函數(PMF),連續隨機變數有相似概念的機率密度函數(PDF): 對於累積分布函數,存在滿足： 那麼X為連續隨機變數，其PDF為...

前言 為了整理數學公式和推導的美觀性，在之前的文章中引入了LaTeX的語法。在編輯器上顯示正常，但當hexo g後生成的網頁中LaTeX語法沒有得到正確渲染。以下將為Hexo添加支持LaTex語法。 注意：有些hexo主題本身就支持LaTeX渲染，根據readme打開即可 歷程 筆者在網路上看了多種...