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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|线性代数代写linear algebra代考|Vector Spaces

A vector space over $\mathbb{K}$ or a linear space over $\mathbb{K}$ is a non-empty set $V$ endowed with the operations of addition $+$ and scalar multiplication $\mu$ addition
\begin{aligned} +: V \times V & \rightarrow V \ (\boldsymbol{u}, \boldsymbol{v}) & \mapsto \boldsymbol{u}+\boldsymbol{v} \end{aligned}
scalar multiplication
\begin{aligned} \mu: \mathbb{K} \times V \rightarrow V \ (\alpha, \boldsymbol{u}) & \mapsto \alpha \boldsymbol{u} \end{aligned}
satisfying, for all $\boldsymbol{u}, \boldsymbol{v}, \boldsymbol{w} \in V$ and $\alpha, \beta \in \mathbb{K}$,
(i) $u+v=v+u$
(ii) $\boldsymbol{u}+(\boldsymbol{v}+\boldsymbol{w})=(\boldsymbol{u}+\boldsymbol{v})+\boldsymbol{w}$
(iii) There exists an element 0 in $V$, called the additive identity, such that
$$u+0=u=0+u$$
(iv) Given $u \in V$, there exists an element $-\boldsymbol{u} \in V$, called the additive inverse of $\boldsymbol{u}$, such that
$$\boldsymbol{u}+(-\boldsymbol{u})=\mathbf{0}=(-\boldsymbol{u})+\boldsymbol{u}$$
(v) $\alpha(\boldsymbol{u}+\boldsymbol{v})=\alpha \boldsymbol{u}+\alpha \boldsymbol{v}$
(vi) $(\alpha \beta) \boldsymbol{u}=\alpha(\beta \boldsymbol{u})$
(vii) $(\alpha+\beta) \boldsymbol{u}=\alpha \boldsymbol{u}+\beta \boldsymbol{u}$
(viii) $1 \boldsymbol{u}=\boldsymbol{u}$
When $\mathbb{K}=\mathbb{R}$ (respectively, $\mathbb{K}=\mathbb{C}$ ), $V$ is also called a real vector space (respectively, a complex vector space).

An element of a vector space is said to be a vector or point. Axioms (i),(ii) say, respectively, that the addition of vectors is commutative and associative. We can also see in (v) and (vii) that the multiplication by a scalar is distributive relative to the addition of vectors and that the multiplication by a vector is distributive relative to the addition of scalars.

## 数学代写|线性代数代写linear algebra代考|Linear Independence

Definition 25 Let $\boldsymbol{u}_1, \boldsymbol{u}_2, \ldots, \boldsymbol{u}_k$ be vectors in a vector space $V$ over $\mathbb{K}$. $A$ linear combination of $\boldsymbol{u}_1, \boldsymbol{u}_2, \ldots, \boldsymbol{u}_k$ is any vector which can be presented as
$$\alpha_1 \boldsymbol{u}_1+\alpha_2 \boldsymbol{u}_2+\cdots+\alpha_k \boldsymbol{u}_k,$$
where $\alpha_1, \alpha_2, \ldots, \alpha_k$ are saclars.
The set $\operatorname{span}\left{\boldsymbol{u}_1, \boldsymbol{u}_2, \ldots, \boldsymbol{u}_k\right}$ consisting of all linear combinations of $\left{\boldsymbol{u}_1, \boldsymbol{u}_2, \ldots, \boldsymbol{u}_k\right}$ is called the span of the vectors $\boldsymbol{u}_1, \boldsymbol{u}_2, \ldots, \boldsymbol{u}_k$, i.e.,
$$\operatorname{span}\left{\boldsymbol{u}_1, \boldsymbol{u}_2, \ldots, \boldsymbol{u}_k\right}=\left{\alpha_1 \boldsymbol{u}_1+\alpha_2 \boldsymbol{u}_2+\cdots+\alpha_k \boldsymbol{u}_k: \alpha_1, \alpha_2, \ldots, \alpha_k \in \mathbb{R}\right}$$
Proposition 3.3 Let $\boldsymbol{u}_1, \boldsymbol{u}_2, \ldots, \boldsymbol{u}_k$ be vectors in a vector space $V$ over $\mathbb{K}$. Then the set $\operatorname{span}\left{\boldsymbol{u}_1, \boldsymbol{u}_2, \ldots, \boldsymbol{u}_k\right}$ is a vector subspace of $V$.

Proof We must show that $\operatorname{span}\left{\boldsymbol{u}_1, \boldsymbol{u}_2, \ldots, \boldsymbol{u}_k\right}$ is a (non-empty) set closed under vector addition and scalar multiplication. We start by showing that $\operatorname{span}\left{\boldsymbol{u}_1, \boldsymbol{u}_2, \ldots, \boldsymbol{u}_k\right}$ is closed for vector addition.

# 线性代数代考

## 数学代写|线性代数代写linear algebra代考|Vector Spaces

$$+: V \times V \rightarrow V(\boldsymbol{u}, \boldsymbol{v}) \quad \mapsto \boldsymbol{u}+\boldsymbol{v}$$

$$\mu: \mathbb{K} \times V \rightarrow V(\alpha, \boldsymbol{u}) \mapsto \alpha \boldsymbol{u}$$

\begin{aligned} &\text { (一) } u+v=v+u \ &\text { (二) } \boldsymbol{u}+(\boldsymbol{v}+\boldsymbol{w})=(\boldsymbol{u}+\boldsymbol{v})+\boldsymbol{w} \end{aligned}
(iii) 存在元素 $0 V$ ，称为加性恒等式，这样
$$u+0=u=0+u$$
(iv) 给定 $u \in V$ ，存在一个元素 $-\boldsymbol{u} \in V$ ，称为加法逆 $\boldsymbol{u}$, 这样
$$\boldsymbol{u}+(-\boldsymbol{u})=\mathbf{0}=(-\boldsymbol{u})+\boldsymbol{u}$$
(在) $\alpha(\boldsymbol{u}+\boldsymbol{v})=\alpha \boldsymbol{u}+\alpha \boldsymbol{v}$
(我们) $(\alpha \beta) \boldsymbol{u}=\alpha(\beta \boldsymbol{u})$
(七) $(\alpha+\beta) \boldsymbol{u}=\alpha \boldsymbol{u}+\beta \boldsymbol{u}$

## 数学代写|线性代数代写linear algebra代考|Linear Independence

$$\alpha_1 \boldsymbol{u}_1+\alpha_2 \boldsymbol{u}_2+\cdots+\alpha_k \boldsymbol{u}_k,$$

$\backslash$ left 的分隔符缺失或无法识别

《left 的分隔符缺失或无法识别

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师