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• Statistical Inference 统计推断
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• (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|代数学代写Algebra代考|Matrices and Matrix Operations

One more concept that we will need before we start running with linear algebra is that of a matrix, which is a $2 \mathrm{D}$ array of numbers like
$$A=\left[\begin{array}{cc} 1 & 3 \ 2 & -1 \end{array}\right] \text { and } B=\left[\begin{array}{ccc} 3 & 0 & 2 \ 0 & -1 & 1 \end{array}\right] \text {. }$$
Note that every row of a matrix must have the same number of entries as every other row, and similarly every column must have the same number of entries as every other column. The rows and columns must line up with each other, and every spot in the matrix (i.e., every intersection of a row and column) must contain an entry. For example, the following are not valid matrices:
$$\left[\begin{array}{ccc} 1 & 2 & 3 \ & 4 & 5 \end{array}\right] \text { and }\left[\begin{array}{cccc} 2 & -3 & & 4 \ & 1 & 2 & 0 \end{array}\right] \text {. }$$
We typically denote matrices by uppercase letters like $A, B, C, \ldots$, and we write their entries via the corresponding lowercase letters, together with subscripts that indicate which row and column (in that order) the entry comes from. For example, if $A$ and $B$ are as above, then $a_{1,2}=3$, since the entry of $A$ in the 1st row and 2 nd column is 3 . Similarly, $a_{2,1}=2$ and $b_{2,3}=1$. The entry in the $i$-th row and $j$-th column is also called its ” $(i, j)$-entry”, and we sometimes alternatively denote it using square brackets like $[A] i, j$. For example, the (2,1)-entry of $B$ is $b_{2,1}=[B]_{2,1}=0$.

The number of rows and columns that a matrix has are collectively referred to as its size, and we always list the number of rows first. For example, the matrix $A$ above has size $2 \times 2$, whereas $B$ has size $2 \times 3$. The set of all real matrices with $m$ rows and $n$ columns is denoted by $\mathcal{M}{m, n}$, or simply by $\mathcal{M}_n$ if $m=n$ (in which case the matrix is called square). So if $A$ and $B$ again refer to the matrices displayed above, then $A \in \mathcal{M}_2$ and $B \in \mathcal{M}{2,3}$.

## 数学代写|代数学代写Algebra代考|Matrix Addition and Scalar Multiplication

We do not yet have a nice geometric interpretation of matrices like we did for vectors (we will develop a geometric understanding of matrices in the next section), but for now we note that we can define addition and scalar multiplication for matrices in the exact same entrywise manner that we did for vectors.

Suppose $A, B \in \mathcal{M}{m, n}$ are matrices and $c \in \mathbb{R}$ is a scalar. Then the sum $A+B$ and scalar multiplication $c A$ are the $m \times n$ matrices whose $(i, j)-$ entries, for each $1 \leq i \leq m$ and $1 \leq j \leq n$, are $$[A+B]{i, j}=a_{i, j}+b_{i, j} \quad \text { and } \quad[c A]{i, j}=c a{i, j},$$
respectively.
We also use $O$ to denote the zero matrix whose entries all equal 0 (or $O_{m, n}$ if we wish to emphasize or clarify that it is $m \times n$, or $O_n$ if it is $n \times n$ ). Similarly, we define matrix subtraction $(A-B=A+(-1) B)$ and the negative of a matrix $(-A=(-1) A)$ in the obvious entrywise ways. There is nothing fancy or surprising about how these matrix operations work, but it is worthwhile to work through a couple of quick examples to make sure that we are comfortable with them.
Suppose $A=\left[\begin{array}{cc}1 & 3 \ 2 & -1\end{array}\right], B=\left[\begin{array}{ll}2 & 1 \ 0 & 1\end{array}\right]$, and $C=\left[\begin{array}{ccc}1 & 0 & 1 \ 0 & -1 & 1\end{array}\right]$. Compute
a) $A+B$,
b) $2 A-3 B$, and
c) $A+2 C$.

# 代数学代写

## 数学代写|代数学代写algebra代考|矩阵与矩阵运算

.

$$A=\left[\begin{array}{cc} 1 & 3 \ 2 & -1 \end{array}\right] \text { and } B=\left[\begin{array}{ccc} 3 & 0 & 2 \ 0 & -1 & 1 \end{array}\right] \text {. }$$

$$\left[\begin{array}{ccc} 1 & 2 & 3 \ & 4 & 5 \end{array}\right] \text { and }\left[\begin{array}{cccc} 2 & -3 & & 4 \ & 1 & 2 & 0 \end{array}\right] \text {. }$$

## 数学代写|代数学代写algebra代考|矩阵加法和标量乘法

.

a) $A+B$，
b) $2 A-3 B$，
c) $A+2 C$

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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