向量的转置乘以该向量等于什么啊?

2025年03月15日 06:42
有5个网友回答
网友(1):

等于1。

ei是单位向量,意味着ei的模(长度)为||ei||=1

∴||ei||²=1 而||ei||²=[ei,ei]=ei^T

(注意这是课本里面的基本定义)

∴[ei,ei]=ei^T·ei=1

扩展资料

R(AB)<=min{R(A),R(B)},非零列向量秩等于1,所以R(AAT)<=1,A和AT相乘肯定有不为零的元素,因为主对角线上是列向量各个元素的平方,它们相乘不是零矩阵,所以R(AAT)>=1,推出R(AAT)=1

变化规律

(1)转置后秩不变

(2)r(A)<=min(m,n),A是m*n型矩阵

(3)r(kA)=r(A),k不等于0

(4)r(A)=0 <=> A=0

(5)r(A+B)<=r(A)+r(B)

(6)r(AB)<=min(r(A),r(B))

(7)r(A)+r(B)-n<=r(AB)

网友(2):

向量模长的平方。就是向量各个元素的平方之和。

网友(3):

ei是单位向量,
意味着ei的模(长度)为||ei||=1,
∴||ei||²=1

而||ei||²=[ei,ei]=ei^T·ei
【注意这是课本里面的基本定义】

∴[ei,ei]=ei^T·ei=1

网友(4):

记 a = (x1, x2, ......, xn)^T
则 a^T a = (x1)^2 + (x2)^2 + ...... +(xn)^2
是一个数。

网友(5):

向量的内积,翻书或者百度自己看

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