证明: 设 A2 = A f A(A-I) - O ,从而由常用结论,rank A + rank(A -1) 乂/ = 4 + (/ — A),由常用结论, n = rank I = rank[A + (/- A)] < rank A + rank(/ - A) = rank A + rank(A 一/) 综上,rank A + rank(A -I) = no 反之,Vcre C\a = Aa + {I...
【答案】：由A2=A可得A(A—I)=0设rank(A)=rrank(A—I)=s则由AB=0知(A-I)的每一个列向量都是以A为系数的方阵的齐次线性方程组的解向量．(Ⅰ) 当r=n时由于齐次线性方程组只有零解做此时A—E=O．即此时rank(A)=nrank(A-I)=0rank(A)+rank(A-I)=n结论成立．(Ⅱ) 当r＜n时...
对diag{A,A-I}做块初等变换可以化到diag{0,I},所以rank(A)+rank(A-I)=rank(I)=n然后A的特征值只能是0,1,几何重数看相应的rank结果一 题目 证明幂等矩阵可对角化为什么由A(A-I)=0就可以得到rank(A)+rank(a-I)=n 为什么就又能知道A的维数是n? 答案 对diag{A,A-I}做块初等变换可以化到diag{...
(b) (i) 根據第(a)段條文配發之股份,將於所有方面與當時同類已發行股份(如有)享有同等權益,惟有關分享相關股息之權益除外。 equitynet.com.hk equitynet.com.hk The Conversion Shares shall, save as provided for in these provisions,rankparipassu in all ...
证明幂等矩阵可对角化为什么由A(A-I)=0就可以得到rank(A)+rank(a-I)=n 为什么就又能知道A的维数是n?
证明幂等矩阵可对角化为什么由A(A-I)=0就可以得到rank(A)+rank(a-I)=n 为什么就又能知道A的维数是n?
【题目】9.设A是域F上n维线性空间V上的线性变换,证明:A是幂等变换的充分必要条件是rank(A) + rank(A -I) =n.
n. relative status v. take or have a position relative to others v. take precedence or surpass others in rank rank的用法和例句: 1.You're gonna make me pullrank, I will pullrank. 你逼我动用职权 我就动给你看 2.So if there's anyrankto pull, it's hers. ...
证(1)由A2=I知 A^2-I=(A+I)(A-I)=0 ,由32题得r(A+I)+r(A-I)≤n又由34题(3)知r(A+I)+r(A-I)≥r(A+I+A-I)=r(A)=n,(因为detA≠0)所以有r(A+I)+r(A-I)=n.(2)因为 A^2=A 所以 0=A^2-A=A(A-T) ,故 r(A)+r(A-I)≤n ,又r(A-I)=r(I-A),...
(2.1) and its generalization to n variables, a square matrix is assigned a rank equal to the number of linearly independent forms that its elements describe. Thus, a nonsingular n× n matrix will have rank n, while a n× n singular matrix will have a rank r less than n. The rank ...