如何在R中得到矩阵的右特征向量?-HowtoobtainrighteigenvectorsofmatrixinR?

Edition : the problem in my question was I've tried to find matrix S from equation 8 but this equation have error.

版本:我的问题是，我试图从公式8中找到矩阵S，但这个方程有误差。

How to directly obtain right eigenvectors of matrix in R ? 'eigen()' gives only left eigenvectors

如何在R中直接获得矩阵的右特征向量?“特征”只给出左特征向量。

Really last edition, I've made big mess here, but this question is really important for me :

最后一版，我搞砸了，但这个问题对我来说很重要:

eigen() provides some matrix of eigenvectors, from function help :

eigen()提供了一些特征向量的矩阵，从函数帮助:

" If ‘r <- eigen(A)’, and ‘V <- r$vectors; lam <- r$values’, then

“如果r <- eigen(A)”和“V <- r$向量”;林<- r美元价值”

                      A = V Lmbd V^(-1)                         

(up to numerical fuzz), where Lmbd =diag(lam)"

(up to数值fuzz)， Lmbd =diag(lam)

that is A V = V Lmbd, where V is matrix now we check it :

这是V = vlmbd, V是矩阵，我们检查一下

set.seed(1)
A<-matrix(rnorm(16),4,4)
Lmbd=diag(eigen(A)$values)
V=eigen(A)$vectors
A%*%V

> A%*%V
                      [,1]                  [,2]          [,3]           [,4]
[1,]  0.0479968+0.5065111i  0.0479968-0.5065111i  0.2000725+0i  0.30290103+0i
[2,] -0.2150354+1.1746298i -0.2150354-1.1746298i -0.4751152+0i -0.76691563+0i
[3,] -0.2536875-0.2877404i -0.2536875+0.2877404i  1.3564475+0i  0.27756026+0i
[4,]  0.9537141-0.0371259i  0.9537141+0.0371259i  0.3245555+0i -0.03050335+0i
> V%*%Lmbd
                      [,1]                  [,2]          [,3]           [,4]
[1,]  0.0479968+0.5065111i  0.0479968-0.5065111i  0.2000725+0i  0.30290103+0i
[2,] -0.2150354+1.1746298i -0.2150354-1.1746298i -0.4751152+0i -0.76691563+0i
[3,] -0.2536875-0.2877404i -0.2536875+0.2877404i  1.3564475+0i  0.27756026+0i
[4,]  0.9537141-0.0371259i  0.9537141+0.0371259i  0.3245555+0i -0.03050335+0i

and I would like to find matrix of right eigenvectors R,
equation which define matrix of left eigenvectors L is :

我想找到右特征向量的矩阵R，定义左特征向量的矩阵L是:

L A  = LambdaM L

equation which define matrix of right eigenvectors R is :

右特征向量R的定义矩阵为:

A R = LambdaM R

and eigen() provides only matrix V:

和eigen()只提供矩阵V:

A V = V Lmbd

I would like to obtain matrix R and LambdaM for real matrix A which may be negative-definite.

我想要得到矩阵R和矩阵A，这可能是负定的。

2 个解决方案

m <- matrix(1:9,nrow=3)
e <- eigen(m)
e1 <- e$vectors
zapsmall((m %*% e1)/e1) ## right e'vec
##          [,1]      [,2] [,3]
## [1,] 16.11684 -1.116844    0
## [2,] 16.11684 -1.116844    0
## [3,] 16.11684 -1.116844    0

eL <- eigen(t(m))    
eL1 <- eL$vectors

zapsmall(t(eL1) %*% m/(t(eL1)))
##          [,1]      [,2]      [,3]
## [1,] 16.116844 16.116844 16.116844
## [2,] -1.116844 -1.116844 -1.116844
## [3,]  0.000000  0.000000  0.000000

lefteigen  <-  function(A){
  return(t(eigen(t(A))$vectors))
}