eigenvector
Scaled, not rotated
An eigenvector is a nonzero vector that, when a linear transformation is applied to it, changes only in scale—not direction.
The scaling factor is the eigenvalue.
Eigenvectors are fundamental in linear algebra, appearing in physics, engineering, and data analysis: The principal components are eigenvectors of the covariance matrix.
Every square matrix has associated eigenvectors that reveal its geometric behavior.
Ordered numerical arrangement
- basisUnderlying support or principle
- spanDistance between endpoints
- orthogonalityState of being independent
- normalizationAdjusting to a standard
rank · dimension · magnitude · determinant · trace · transpose · conjugate
Climbing or resizing
- stretchingExtending muscles or material
- operatorOne who works machinery
- projectionSomething that extends outward
- shearLateral sliding force
Reducing to diagonal form
- orthonormalPerpendicular and unit-length
- multiplicityState of being many
matrix
Ordered numerical arrangement
- basisUnderlying support or principle
- spanDistance between endpoints
- orthogonalityState of being independent
normalization · rank · dimension · magnitude · determinant · trace · transpose · conjugate
scaling
Climbing or resizing
- stretchingExtending muscles or material
- operatorOne who works machinery
- projectionSomething that extends outward
diagonalization
Reducing to diagonal form
- orthonormalPerpendicular and unit-length
- multiplicityState of being many
PageRank
Link-based webpage ordering method
- math conceptsangle, numbers, algebra, circle, equations
- linear algebramatrix, linear equation, vectors, linear function, matrices
- operator theoryoperator, adjoint, spectrum, kernel, range
- dimensionality reductionPCA, loading, component, factors, embedding
- eigenvalueseigendecomposition, diagonalization, multiplicity
- vector spacesbasis, dimension, subspace, linear independence, orthogonality