different between eigenvector vs eigenbasis

English

Etymology

eigen- +? vector, a partial calque of German Eigenvektor.

Pronunciation

Noun

eigenvector (plural eigenvectors)

1. (linear algebra) given a linear transformation ${\displaystyle T}$, a vector ${\displaystyle x}$ such that ${\displaystyle Ax=\lambda x}$ for some scalar ${\displaystyle \lambda }$
2. (linear algebra) specifically, given a matrix A, the eigenvector of the transformation "left-side multiplication by A"

Synonyms

• latent vector, proper vector
• characteristic vector

Related terms

• eigendecomposition
• eigenfunction
• eigenspace
• eigenspinor
• eigenstate
• eigenvalue

Derived terms

• eigenvectorial
• left eigenvector
• right eigenvector

Translations

See also

• Mathworld article on eigenvectors

Dutch

Etymology

From eigen +? vector, calque of German Eigenvektor.

Pronunciation

• IPA^(key): /??i?.??n?v?k.t?r/
• Hyphenation: ei?gen?vec?tor

Noun

eigenvector m (plural eigenvectoren)

1. (linear algebra) eigenvector

Spanish

Noun

eigenvector m (plural eigenvectores)

1. (linear algebra) eigenvector

   Synonyms: autovector, vector propio

English

Etymology

eigen- +? basis

Noun

eigenbasis (plural eigenbases)

1. (mathematics) A basis for a vector space consisting entirely of eigenvectors.