eigenvector love

# eigenvector

## Definitions

### from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A vector whose direction is unchanged by a given transformation and whose magnitude is changed by a factor corresponding to that vector's eigenvalue. In quantum mechanics, the transformations involved are operators corresponding to a physical system's observables. The eigenvectors correspond to possible states of the system, and the eigenvalues to possible observed values.

• noun linear algebra A vector that is not rotated under a given linear transformation; a left or right eigenvector depending on context.
• noun physics, engineering 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

### from The American Heritage® Dictionary of the English Language, 4th Edition

[Partial translation of German Eigenvektor : eigen-, characteristic; see eigenvalue + Vektor, vector.]

eigen- +‎ vector

## 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.

• Î£ci  fi, for some set {ci} of complex numbers, where fi, the so-called 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. [

Measurement in Quantum Theory Krips, Henry 2007

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

Sure, sure. 2009

• Also: “why infomercials still exist” eigenvector Says:

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

• 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.

• 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.

• Knowing how to calculate the eigenvector centrality of something is not novel.