### 数学代写|计算线性代数代写Computational Linear Algebra代考|МАTH 1014

statistics-lab™ 为您的留学生涯保驾护航 在代写计算线性代数Computational Linear Algebra方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写计算线性代数Computational Linear Algebra代写方面经验极为丰富，各种代写计算线性代数Computational Linear Algebra相关的作业也就用不着说。

• 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|计算线性代数代写Computational Linear Algebra代考|Axiomatic System

A concept is said to be primitive when it cannot be rigorously defined since its meaning is intrinsically clear. An axiom or postulate is a premise or a starting point for reasoning. Thus, an axiom is a statement which appears unequivocally true and that does not require any proof to be verified but cannot be, in any way, falsified.
Primitive concepts and axioms compose the axiomatic system. The axiomatic system is the ground onto the entire mathematics is built. On the basis of this ground, a definition is a statement that introduces a new concept/object by using previously known concepts (and thus primitive concepts are necessary for defining new ones). When the knowledge can be extended on the basis of previously established statements, this knowledge extension is named theorem. The previously known statements are the hypotheses while the extension is the thesis. A theorem can be expressed in the form: “if the hypotheses are verified then the thesis occurs”. In some cases, the theorem is symmetric, i.e. besides being true that “if the hypotheses are verified then the thesis occurs” it is also true that “if the thesis is verified then the hypotheses occur”. More exactly, if $A$ and $B$ are two statements, a theorem of this kind can be expressed as “if $A$ is verified than $B$ occurs and if $B$ is verified then A occurs”. In other words the two statements are equivalent since the truth of one of them automatically causes the truth of the other. In this book, theorems of this kind will be expressed in the form ” $A$ is verified if and only if $B$ is verified”.

The set of logical steps to deduce the thesis on the basis of the hypotheses is here referred as mathematical proof or simply proof. A large number of proof strategies exist. In this book, we will use only the direct proof, i.e. from the hypotheses we will logically arrive to the thesis or by contradiction (or reductio ad absurdum), i.e. the negated thesis will be new hypothesis that will lead to a paradox. A successful proof is indicated with the symbol $\quad \square$. It must be remarked that a theorem that states the equivalence of two facts requires two proofs. More specifically, a theorem of the kind ‘ $A$ is verified if and only if $B$ is verified” is essentially two theorems in one. Hence, the statements “if $A$ is verified than $B$ occurs” and “if $B$ is verified then $A$ occurs” require two separate proofs.

A theorem that enhances the knowledge by achieving a minor result that is then usable to prove a major result is called lemma while a minor result that uses a major theorem to be proved is called corollary. A proved result that is not as important as a theorem is called proposition.

## 数学代写|计算线性代数代写Computational Linear Algebra代考|Order and Equivalence

Definition 1.15. Order Relation. Let us consider a set $A$ and a relation $\mathscr{R}$ on $A$. This relation is said order relation and is indicated with $\preceq$ if the following properties are verified.

• reflexivity: $\forall x \in A: x \preceq x$
• transitivity: $\forall x, y, z \in A:$ if $x \preceq y$ and $y \preceq z$ then $x \preceq z$
• antisymmetry: $\forall x, y \in A:$ if $x \preceq y$ then $y \not x$
The set $A$, on which the order relation $\preceq$ is valid, is said totally ordered set.
Example 1.4. If we consider a group of people we can always sort them according theirs age. Hence the relation “to not be older than” (i.e. to be younger or to have the same age) with a set of people is a totally ordered set since every group of people can be fully sorted on the basis of their age.

From the definition above, the order relation can be interpreted as a predicate to be defined over the elements of a set. Although this is not wrong, we must recall that, rigorously, a relation is a set and an order relation is a set with some properties. In order to emphasise this fact, let us give again the definition of order relation by using a different notation.

Definition 1.16. Order Relation (Set Notation). Let us consider a set $A$ and the Cartesian product $A \times A=A^{2}$. Let $\mathscr{R}$ be a relation on $A$, that is $\mathscr{R} \subseteq A^{2}$. This relation is said order relation if the following properties are verified for the set $\mathscr{R}$.

## 数学代写|计算线性代数代写Computational Linear Algebra代考|Functions

Definition 1.23. Function. A relation is said to be a mapping or function when it relates to any element of a set a unique element of another. Let $A$ and $B$ be two sets, a mapping $f: A \rightarrow B$ is a relation $\mathscr{R} \subseteq A \times B$ such that $\forall x \in A, \forall y_{1}$ and $y_{2} \in B$ it follows that

• $\left(x, y_{1}\right) \in f$ and $\left(x, y_{2}\right) \in f \Rightarrow y_{1}=y_{2}$
• $\forall x \in A: \exists y \in B \mid(x, y) \in f$
where the symbol : $A \rightarrow B$ indicates that the mapping puts into relationship the set $A$ and the set $B$ and should be read “from $A$ to $B$ “, while $\Rightarrow$ indicates the material implications and should be read “it follows that”. In addition, the concept $(x, y) \in f$ can be also expressed as $y=f(x)$.
An alternative definition of function is the following.
Definition 1.24. Let $A$ and $B$ be two sets, a mapping $f: A \rightarrow B$ is a relation $\mathscr{R} \subseteq$ $A \times B \mid$ that satisfies the following property: $\forall x \in A$ it follows that $\exists ! y \in B$ such that $(x, y) \in \mathscr{R}$ (or, equivalently $y=f(x)$ ).

Example 1.12. The latter two definitions tell us that for example $(2,3)$ and $(2,6)$ cannot be both element of a function. We can express the same concept by stating that if $f(2)=3$ then it cannot happen that $f(2)=6$. In other words, if we fix $x=2$ then we can have only one $y$ value such that $y=f(x)$.

Thus, although functions are often interpreted as “laws” that connect two sets, mathematically, a function is any set (subset of a Cartesian product) for which the property in Definition $1.24$ is valid.

## 数学代写|计算线性代数代写Computational Linear Algebra代考|Order and Equivalence

-反身性: $\forall x \in A: x \preceq x$

• 传递性: $\forall x, y, z \in A$ :如果 $x \preceq y$ 和 $y \preceq z$ 然后 $x \preceq z$
• 反对称: $\forall x, y \in A$ :如果 $x \preceq y$ 然后 $y \not x$
套装 $A$ ，其上的顺序关系了是有效的，就是说全序集。
例 1.4。如果我们考虑一组人，我们总是可以根据他们的年龄对他们进行排序。因此，与一组人的“不比”（即 年轻或具有相同年龄) 的关系是一个完全有序的集合，因为每组人都可以根据他们的年龄进行完全排序。
根据上面的定义，顺序关系可以解释为要在集合的元素上定义的谓词。虽然这没有错，但我们必须记住，严格地 说，关系是一个集合，而顺序关系是一个具有某些属性的集合。为了强调这一事实，让我们使用不同的符号再次给 出顺序关系的定义。
定义 1.16。顺序关系 (集合符号)。让我们考虑一个集合 $A$ 和笛卡尔积 $A \times A=A^{2}$. 让 $\mathscr{R}$ 成为关系 $A$ ，那是 $\mathscr{R} \subseteq A^{2}$. 如果为集合验证了以下属性，则该关系称为顺序关系 $\mathscr{R}$.

## 数学代写|计算线性代数代写Computational Linear Algebra代考|Functions

• $\left(x, y_{1}\right) \in f$ 和 $\left(x, y_{2}\right) \in f \Rightarrow y_{1}=y_{2}$
• $\forall x \in A: \exists y \in B \mid(x, y) \in f$ 读“它遵循”。此外，概念 $(x, y) \in f$ 也可以表示为 $y=f(x)$.
函数的另一种定义如下。
定义 1.24。让 $A$ 和 $B$ 是两个集合，一个映射 $f: A \rightarrow B$ 是关系 $\mathscr{R} \subseteq A \times B \mid$ 满足以下性质: $\forall x \in A$ 它遵 循 $\exists ! y \in B$ 这样 $(x, y) \in \mathscr{R}$ (或者，等效地 $y=f(x)$ ).
示例 1.12。后两个定义告诉我们，例如 $(2,3)$ 和 $(2,6)$ 不能同时是函数的元素。我们可以表达同样的概念，如果 $f(2)=3$ 那么它不可能发生 $f(2)=6$. 换句话说，如果我们修复 $x=2$ 那么我们只能有一个 $y$ 值使得 $y=f(x)$.
因此，尽管函数通常被解释为连接两个集合的“定律”，但在数学上，函数是定义中的属性的任何集合（笛卡尔积的 子集） $1.24$ 已验证。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。