Finding dominant eigenvector and eigenvalue

Question

I calculated the eigen of a matrix:

e <- eigen(t)

Now I need to get the dominant eigenvalue and dominant eigenvector

Is the dominant eigenvalue calculated:

e$values[1]

And what about the dominant eigenvector? Is it extracted by:

e$vectors[,1]

I am asking since I thought that e$values will give me the eigenvalues from largest to smallest...but I am getting these results:

 [1]  1.000000e+00  3.751736e-01  3.751736e-01 -4.143304e-01 -4.143304e-01
 [6] -4.330604e-01 -4.330604e-01 -7.921977e-02 -7.921977e-02  5.948138e-02
[11]  5.948138e-02  6.969758e-04  6.969758e-04 -4.057858e-02 -4.057858e-02
[16]  3.039333e-02  3.039333e-02  8.007672e-03  8.007672e-03 -2.005426e-02
[21] -2.005426e-02  2.361154e-02  2.361154e-02  1.023211e-02  1.023211e-02
[26]  1.099767e-02  1.099767e-02 -9.547037e-03 -9.547037e-03  1.070972e-02
[31]  1.070972e-02 -1.925037e-03 -1.925037e-03 -2.908073e-03 -2.908073e-03
[36]  1.517843e-04  1.517843e-04 -1.088992e-04 -3.070693e-10  3.070676e-10

denis denis · Accepted Answer · 2018-02-24T20:20:49

from the help function:

values

a vector containing the (p) eigenvalues of x, sorted in decreasing order, according to Mod(values) in the asymmetric case when they might be complex (even for real matrices). For real asymmetric matrices the vector will be complex only if complex conjugate pairs of eigenvalues are detected. vectors

either a (p\times p) matrix whose columns contain the eigenvectors of x, or NULL if only.values is TRUE. The vectors are normalized to unit length.

It says decreasing order, and a matrix whose column contain the vectors, so yes it would be

e$values[1]
e$vectors[,1]

Dont't forget that if you want more help, you should provide an reproducible example in order us to understand what's wrong

Finding dominant eigenvector and eigenvalue

1 Answers