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

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我们提供的计算线性代数Computational Linear Algebra及其相关学科的代写,服务范围广, 其中包括但不限于:

  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等概率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (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|МАTH 1014

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|МАTH 1014


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


在假设的基础上推导出论文的一组逻辑步骤在这里被称为数学证明或简称证明。存在大量的证明策略。在本书中,我们将仅使用直接证明,即从逻辑上我们将通过矛盾(或归约法)得出命题的假设,即被否定的命题将是会导致悖论的新假设。成功的证明用符号表示. 必须指出,陈述两个事实等价的定理需要两个证明。更具体地说,一种定理 ‘一个当且仅当被验证乙被验证”本质上是两个定理合二为一。因此,陈述“如果一个验证比乙发生”和“如果乙然后验证一个发生”需要两个单独的证明。


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

定义 1.15。订单关系。让我们考虑一个集合 $A$ 和一个关系肩上 $A$. 这种关系称为顺序关系并用く如果验证了以下属 性。
-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

定义 1.23。功能。当关系与集合中的任何元素或另一个元素的唯一元素相关时,它就被称为映射或函数。让 $A$ 和 $B$ 是两个集合,一个映射 $f: A \rightarrow B$ 是关系 $\mathscr{R} \subseteq A \times B$ 这样 $\forall x \in A, \forall y_{1}$ 和 $y_{2} \in B$ 它遵循

  • $\left(x, y_{1}\right) \in f$ 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 $y=f(x)$.
    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。
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术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。



有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。





随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。


多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。


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。