Suppose a random matrix $A$ with its elements following Gaussian distribution with non-zero mean. We know that the eigenvalues of $A$ have two patches: one is at the real axis that is far away from the origin point, and the other one is a circle around the origin point. We know that the eigenvector of the first patch is $[1,1,\cdots,1]$, but what is the distribution of the elements of an eigenvector whose corresponding eigenvalue is in the second patch?
The distribution of the elements of an eigenvector of random matrices
Zedong Bi
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