Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. A vector that is not rotated under a given linear transformation; a left or right eigenvector depending on context.
 n. A right eigenvector; a nonzero vector such that, for a particular matrix , for some scalar which is its eigenvalue and an eigenvalue of the matrix.
Etymologies
Examples

The concept of increased positive standard of living is a valuable measure, but it is not a "eigenvector" of the economy in any sense.
Evolutionary Psychology and Economic Bias, Bryan Caplan  EconLog  Library of Economics and Liberty

Î£ci fi, for some set {ci} of complex numbers, where fi, the socalled eigenvector of Q corresponding to possible value qi, is that state of S at t for which, when S is in that state, there is unit probability that Q has value qi. [

The real budget in the final answer, in Greg's paper, is output from labor, socialness, and height; a three eigenvector decomposition of the general set of economies consisting of random draws according the the presented probaility distributions.
Mankiw Defends his Tall Tale, Arnold Kling  EconLog  Library of Economics and Liberty

The curve typically indicates a nonlinear correlation; i.e. more authenticity generates an increasingly trusting relationship. eigenvector Says:

Also: “why infomercials still exist” eigenvector Says:

Hey, I think Jo must be a pigeon. eigenvector Says:

But it is indeed always the pushing that counts. eigenvector Says:

Why, just create a matrix of the links and then an eigenvector of that matrix is the answer.

Knowing how to calculate the eigenvector centrality of something is not novel.
The Volokh Conspiracy » Supreme Court Skeptical of Business Method Patents

These discussions are sliced and diced using things like eigenvector centrality to determine patterns and opinions for a range of clients from Fortune 500 companies to government TLAs.
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machineplay commented on the word eigenvector
eigenvector: There was a time when I knew what this word meant  just enough to know I'd never really be able to use one.
December 7, 2006