Try Our Apps


Pore Over vs. Pour Over


[ahy-guh n-vek-ter] /ˈaɪ gənˌvɛk tər/
noun, Mathematics
Origin of eigenvector
1955-60; < German Eigenvektor Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2015.
Cite This Source
British Dictionary definitions for eigenvector


(maths, physics) a vector x satisfying an equation Ax = λx, where A is a square matrix and λ is a constant
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
Cite This Source
eigenvector in Technology
A vector which, when acted on by a particular linear transformation, produces a scalar multiple of the original vector. The scalar in question is called the eigenvalue corresponding to this eigenvector.
It should be noted that "vector" here means "element of a vector space" which can include many mathematical entities. Ordinary vectors are elements of a vector space, and multiplication by a matrix is a linear transformation on them; smooth functions "are vectors", and many partial differential operators are linear transformations on the space of such functions; quantum-mechanical states "are vectors", and observables are linear transformations on the state space.
An important theorem says, roughly, that certain linear transformations have enough eigenvectors that they form a basis of the whole vector states. This is why Fourier analysis works, and why in quantum mechanics every state is a superposition of eigenstates of observables.
An eigenvector is a (representative member of a) fixed point of the map on the projective plane induced by a linear map.
The Free On-line Dictionary of Computing, © Denis Howe 2010
Cite This Source

Word of the Day

Difficulty index for eigenvector

Few English speakers likely know this word

Word Value for eigenvector

Scrabble Words With Friends

Nearby words for eigenvector