AI engineering glossary · Linear algebra
What is eigenvector?
Eigenvector (also called Characteristic vector): A non-zero vector that a matrix only rescales, never rotates: A v = lambda v, where lambda is its eigenvalue. Eigenvectors mark the natural axes of a transformation, such as the directions of greatest variance in a covariance matrix.
Eigenvector: an example
For A = [[2,0],[0,3]], v = [1, 0] gives A v = [2, 0] = 2 v, so v is an eigenvector with eigenvalue 2.
Related terms
More Linear algebra terms
- Einstein summation
- Frobenius norm
- Full rank
- Gaussian elimination
- Gram matrix
- Gram-Schmidt process
- Hadamard product
- Homogeneous coordinates
Where you learn it
Eigenvector is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.