Chapter 1 Vector Algebra ♦ Vector Space Vector and vector space A vector is described as a quantity that has both direction and length.  A vector space is a collection of these geometic objects that can be added together and multiplied by numbers. Wh…

I. 范数(Norm) 定义: 向量空间\(V\)上的范数(norm)是如下函数: \[ \begin{align} \|·\|:V→R, \notag \\ x→\|x\| \notag \end{align} \] 该函数会赋予每个向量\(x\)自身的长度\(\|x\|∈R\),并且对于\(\lambda∈R,\,\,x,y∈V\)满足如下性质: Absolutely homogeneous:\(\|\lambda x\|=|\lambda|\|x\|\) Triangle inequali…

♦Linear map Definition Linear map A linear map from vector space V to W over a field F is a function T with the following properties: Additivity: T(u+v)=T(u)+T(v) for every u,v∈V. Homogeneity: T(λv)=λT(v) for v∈V and λ∈F. Example Linear map zero In a…

Chapter2 Numerical sequence and function Cartesian product set If S and T are sets,then the cartesian product set S×T is formed by taking all ordered pairs (p,q) where p∈S and q∈T. Relations,functions Any subject f of the cartesian product S×T is cal…

<国外优秀数学教材选评>推荐书目下载 具体内容请查看原内容: http://www.library.fudan.edu.cn/wjzx/list/373-1-20.htm 或者http://202.120.227.7/wjzx/list/373-1-20.htm 注: 由于国外教材更新频繁,其中非数学专业教材尤为显著,相较于原版本,其中有部分版本已经更新,以下提供的是尽所能搜索到的最新版本 所有文件都来源网络,余不敢独享,特整理发布.尽力择高质量版本分享,但难免有所疏漏,烦请提出宝贵意见 由于…

1.老老实实把课本上的题目做完.其实说科大的课本难,我以为这话不完整.科大的教材,就数学系而言还是讲得挺清楚的,难的是后面的习题.事实上做1道难题的收获是做10道简单题所不能比的. 2.每门数学必修课至少要看一本参考书,尽量做一本习题集. 3.数学分析别做吉米,除非你太无聊,推荐北大方企勤的习题集.此外注意一下有套波兰的数学分析习题集,是不是搞得到中文或英文版. 4.线性代数推荐普罗斯库列科夫的<<线性代数习题集>>和法捷耶夫的<<高等代数习题集>>.莫斯科…

NI Vision 控件模板 Vision控件模板位于LabVIEW控件模板的最顶层,由一下元素组成: IMAQ Image.ctl—该控件是一个类型定义,用于声明图象类型的数据.在VI的前面板中使用该控件代表图象类型数据.例如,使用该控件作为一个子程序的输入或输出,使调用成成可以将一幅图像传送给子程序. 图像显示(Image Display)—该控件用于在LabVIEW 中直接显示图像.也可以利用该控件创建关注区域 (ROIs). 图像显示控件提供标准和3D版两种外观. IMAQ 视觉控件(I…

总结: 1.线性变换运算封闭,加法和乘法 2.特征向量经过线性变换后方向不变 https://en.wikipedia.org/wiki/Linear_map Examples of linear transformation matrices In two-dimensional space R2 linear maps are described by 2 × 2 real matrices. These are some examples: rotation by 90 degrees c…

8.02  Physics II (电磁学基础) Introduction to electromagnetism and electrostatics: electric charge, Coulomb's law, electric structure of matter; conductors and dielectrics. Concepts of electrostatic field and potential, electrostatic energy. Electric curr…

<Differential Geometry of Curves and Surfaces> by Manfredo P. do Carmo real line Rinterval I==============================================CH1 CurvesDEFINITION. A parametrized differentiable curve is a differentiable map a: I --> R3 of [an open in…