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.
from Wiktionary, Creative Commons Attribution/Share-Alike License.
- noun linear algebra A
vector that is not rotated under a givenlinear 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 somescalar which is itseigenvalue and aneigenvalue of the matrix.
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/Share-Alike License
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Examples
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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 2009
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Σci 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
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The curve typically indicates a non-linear correlation; i.e. more authenticity generates an increasingly trusting relationship. eigenvector Says:
Sure, sure. 2009
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Also: “why infomercials still exist” eigenvector Says:
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Hey, I think Jo must be a pigeon. eigenvector Says:
Do not feed them. 2009
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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 2009
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But it is indeed always the pushing that counts. eigenvector Says:
How to get unstuck. 2010
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Why, just create a matrix of the links and then an eigenvector of that matrix is the answer.
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Knowing how to calculate the eigenvector centrality of something is not novel.
The Volokh Conspiracy » Supreme Court Skeptical of Business Method Patents 2009
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Knowing how to calculate the eigenvector centrality of something is not novel.
The Volokh Conspiracy » Supreme Court Skeptical of Business Method Patents 2009
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