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eigenvector (plural eigenvectors)
- (linear algebra) A vector that is not rotated under a particular linear transformation; a left or right eigenvector depending on context; (more formally) given a linear transformation A, a vector x such that Ax=λx [or xA=λx] for some scalar λ (called the eigenvalue).
- (physics, engineering) A right eigenvector; given a matrix A, the eigenvector of the transformation "left-side multiplication by A."
- Eigenvector has become the standard term in English, but proper vector was formerly more common.
- The concepts of eigenvector and eigenvalue arose from the study of quadratic forms and differential equations. Nowadays, they are normally introduced in the context oflinear algebra.
- A linear transformation can always be represented as a matrix if the vector space is finite-dimensional (usually a safe assumption in physics).
- In consequence of the rules of matrix multiplication, left eigenvectors are row vectors, while right eigenvectors are column vectors. The convention of right eigenvector as "standard" is fundamentally an arbitrary choice.
vector not rotated by linear transformation
eigenvector m (plural eigenvectoren)
eigenvector m (plural eigenvectores)