Definitions – Digital Signature - a data string which associates a message with some originating entity – Digital Signature Generation Algorithm – a method for producing a digital signature – Digital signature verification algorithm - a method for verifying that a digital signature is authentic (i.e., was indeed created by the specified entity)

2.3逆矩阵 定义:对于Ann,若有Bn满足AB=BA=E,则称A为可逆矩阵, 且B为A的逆矩阵,记作A-1=B. 定理1若A为可逆矩阵,则A的逆矩阵唯一 证设B与C都是A的逆矩阵,则有

第三章3-2n阶方阵的行列式(续) 3.2.5行列式的按任意列展开和特殊矩阵的行列式 1、行列式的按任意行(列)展开 定义命A=(-1)M,称为a的代数余子式 = 命题按行列式的第i行展开,有 证明将第i行先后与第i-1,i-2,…,1行交换,再展开。 推论行列式按第j行展开,有a=a 2、范德蒙行列式 形如 111 |= a1a2…an an 的行列式称为范德蒙行列式

Modified atmosphere packaging(map) is widely used for many food products and is now a commercial and economic reality. MAP is common in markets that have a well established and controlled cold chain and that can sustain a high- priced quality product. However, MAP is a mild preservation method and a major concern is that MAP storage may not provide a sufficient level of safety for the extended storage of fresh chilled food products with regard to pathogenic

1.复数列的极限设{an}(n=12)为一复数列 ,其中an=an+ibn,又设a=a+ib为一确定的复数 如果任意给定ε0,相应地能找到一个正数 N(a),使|an-aN时成立,则a称为复数 列{an}当n→∞时的极限,记作 linn =a

一、相似矩阵与相似变换的概念 定义1设A,B都是n阶矩阵若有可逆矩阵P,使 P-AP= B, 则称B是A的相似矩阵或说矩阵A与B相似对A进 行运算P-1AP称为对A进行相似变换可逆矩阵P 称为把A变成B的相似变换矩阵

一、选择题 A型题 1.e2.b3.c4.c5.a6.c7.8.c9.b10.be 12.c13.a14.d15.e16.b17.e18.e19.a20.21.22. 23.b24.a25.c26.c27.b28.c29.a30.c31.c32.d33.b

第五章5-1双线性函数 5.1.1线性空间上的线性函数的定义 1、线性函数的定义 定义设V为数域K上的线性空间,fV→K为映射,满足 f(a+B)=f(a)+f(),va,B∈V;f(ka)kf(a),∈k,aev,则称f为由V 到K的一个线性函数(即f为V到K的一个线性映射) 如同一般的线性映射,有以下事实: i)、f:V→K是线性函数当且仅当f(ka+1B)=kf(a)+lf(B) i)、f(0)=0; i)、f(-a)=-f(a) 命题数域K上的n维线性空间V上的线性函数的全体关于函数加法和数乘构成K上 的n维线性空间

A real, an imaginary, or a complex forcing function will produce a real, an imaginary, or complex response, respectively. Instead of applying a real forcing function to obtain the desired real response, we apply a complex forcing function whose real part is the given real forcing function; we obtain a complex response whose real part is the desired real response

Intensive Study There's a Lot More to Life than a Job Para.1 It has often been remarked that the saddest thing about youth is that it is wasted on the young. Para. 2 Reading a survey report on first-year college students, I recalled the regret, \If only knew then what know now