eigenvector

E e

Transcription

- US Pronunciation
- US IPA
- UK Pronunciation
- UK IPA
- \-ˌvek-tər\
- /eɪɪnˈvektər/

- US Pronunciation
- US IPA
- \-ˌvek-tər\

Definitions of eigenvector word

noun eigenvector A vector that when operated on by a given operator gives a scalar multiple of itself. 1
noun Definition of eigenvector in Technology (mathematics) 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. 1
noun eigenvector a vector x satisfying an equation Ax = λx, where A is a square matrix and λ is a constant 0

See all 3 definitions of eigenvector

Information block about the term

Parts of speech for Eigenvector

noun

adjective

verb

adverb

pronoun

preposition

conjunction

determiner

exclamation

Full grammatical hierarchy of Eigenvector

eigenvector popularity

This term is known only to a narrow circle of people with rare knowledge. Only 7% of English native speakers know the meaning of this word.

This word is included in each student's vocabulary. Most likely there is at least one movie with this word in the title.

eigenvector usage trend in Literature

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