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设A是n维欧氏空间V内的一个线性变换,如果对a,∈V,都有 (Aa,)=(a, AB) 则称A是V内的对称变换 命题n维欧氏空间V上的线性变换A是对称变换当且仅当它在标准正交基 ,2n下的矩阵A是实对称矩阵
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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)
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第四章线性空间与线性变换 4-1线性空间的基本概念 4.1.1线性空间的定义及例 1、线性空间的定义 定义4.1线性空间 设V是一个非空集合,且V上有一个二元运算“+”(V×V→V),又设K为数域,V中的元素与K中的元素有运算数量乘法“·”(K×V→V),且“+”与“·”满足如下性质: 1、加法交换律a,B∈V,有a+B=B+a; 2、加法结合律a,B,y∈V,有(a+B)+y=a+(B+y)
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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
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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
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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
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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
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一、集合 集合是数学中最基本的概念之一,所谓集合就是指作为整体看的一堆东西 组成集合的东西称为这个集合的元素用 a∈M 表示a是集合M的元素,读为:a属于M用 a∈M 表示a不是集合M的元素,读为:a不属于M 所谓给出一个集合就是规定这个集合是由哪些元素组成的因此给出一个集 合的方式不外两种,一种是列举法:列举出它全部的元素,一种是描述法:给出这个集合的元素所具有的特征性质
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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
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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
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