三阶矩阵A= 1 -1 2 0 -5 6 0 1 0 求该矩阵的N次幂。 PS： 这是个亏损矩阵 不能对角化

Posted 2023-03-28

问题现在可以简化成这样
就是矩阵A和JORDAN型相似
怎么求那个过度矩阵T 使得T-¹AT=JORDAN型

首先它的特征值是1,1,-6
然后Ax=-6x的解是(8,-42,-7)
Ax=x的解有（1,0,0）
然后再取一个和(1,1,-6)正交同时不正比于(1,0,0)的，比如（1,-1,0）
T的列向量就都就出来了 参考技术A 不能对角化~~~这个 ~~思考一下

A为三阶矩阵,E为三阶单位矩阵A的三个特征值分别为1,2,-3,则下列矩阵中是可逆矩阵的是: A.A-E B.A+E C.A+3E

A为三阶矩阵,E为三阶单位矩阵A的三个特征值分别为1,2,-3,则下列矩阵中是可逆矩阵的是: A.A-E B.A+E C.A+3E D.A-2E 为什么答案是B？

若要A+aE可逆，只需|A+aE|≠0，即a不是-A的特征值，亦即-a不是A的特征值。因此a≠-1，-2,3即可。观察选项，只有A+E可逆，选B。 参考技术A Maria Sharapova

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Colavito WTA baby is no doubt the hottest star on the track, get to the last 4 at Wimbledon last year,InStyler Hair Crimping Iron, she went further in his career this year's initial Grand Slam final track, although the final opponent is has three Grand Slam titles and struggle with their own take advantage of Sharapova, but still feel very confident Colavito baby, On this final Sunday when she was bold to point out their benefits where: "Obviously I serve is a big advantage, I love to serve immediately after the attack, and that i love watching men's tennis match,Hair Straightener, Del Potro has been my favorite player, we play much like the , hit the ball very quickly and incredibly flat. "

Colavito also stated he's presently small baby don't really feel nervous, she will 't be in the race for the ear-piercing screams Sharapova feel any be concerned: "I didn't feel any tension, on the contrary I am getting excited about this final I now sleep well and I such as the grass court battle, it can maximize my technical characteristics, so I made a great record. In addition, I don't worry about stadium noise issues, after i entered the race I'd not think about other activities, but simply to focus on their game. semifinal game and that i Azarenka she'll scream, however i don't care,good hair straighteners, I really don't even think it'll bring a lot impact. " 参考技术B 原因很简单，由Jordan标准化知，A可看作上三角阵，对角线值为1,2,-3.detA=-6.
所以det(A-E)=det(A+3E)=det(A-2E)=0，而det(A+E)=-12<0. 故只有A+E可逆. 参考技术C |A|的值为三个特征值的乘积，当|A|不为0，则矩阵的秩为3，可逆
|A-E|=（1-1）（2-1）（-3-1）=0
|A+E|=（1+1）（2+1）（-3+1）不为0，选B