线性函数 定义1设V是数域P上的一个线性空间,f是V到P的一个映射,如果f 满足 1)f(a+)=f(a)+f() 2) f(ka)=(a), 式中a,B是V中任意元素,k是P中任意数,则称f为V上的一个线性函数 从定义可推出线性函数的以下简单性质: 1.设f是v上的线性函数,则f(0)=0,f(-a)=-f(a) 2.如果B是a1,a2…,a的线性组合:

Chapter 2 The Particle in a Box 2.1 Differential Equations (linear) A (x)+An-(x)y (n-1) +…+Ay=g(x)

例3设n阶方阵A的伴随矩阵为A*,证明: (1)若A=0,则A=0 (2)a=ain-1 证明:由伴随矩阵的定义显然有 AA*=AA=AIEn, 两边取行列式即得 JAllAdet()=a, 故当A不等于0时,(2)是显然的。而 只要我们证明了(1),则(2)对于A|=0 的矩阵A也是成立的。下面我们证明(1)

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(ⅡI)形如 =fax+b+c a,x+b,+c 的方程, 其中a,a,b2,,2均为实常数

3.1.1平行四边形的有向面积和平行六面体的有向体积具有的三条性质 在解析几何中已证明,给定二维向量空间中的单位正交标架,设向量a,B的坐标分别 为(a1,a2)和(b,b2),则由向量a,B张成的平行四边形的有向面积为ab2-a2b,这里记 为;给定三维空间内右手单位正交标架,设向量a,B,y的坐标分别为(a1,a2,a3)

8.1. Independent Firms The downstream firm's problem is max(a-bxc-wT The upstream firm's problem is max(a-2b)3-cr The output is 8.2. Integrated Firm Suppose now that the two firms merge into one firm. This firms problem is max(a-by)y

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Chapter 12 Time Series Analysis 12.1 Stochastic processes A stochastic process is a family of random variables {Xt,t ET}. Example{St,t 0, 1,2,...} where St i=o X; and iid(0,2). St has a different distribution at each point t

A function is a term used in mathematics and logic to denote a relationship between input and output variables. Each variable is restricted to binary (0, 1) values The relationship is the complex of three primitive functions (And \\Not\\Or)