eigenvectors
Scaling-only transformation survivors
Eigenvectors are vectors that, when a linear transformation is applied to them, change only in scale—not direction.
The scalar by which an eigenvector stretches or shrinks is its eigenvalue.
These concepts are fundamental in linear algebra and appear throughout physics, engineering, and data science: The eigenvectors of the covariance matrix reveal the principal components.
Singular: eigenvector.
Ordered numerical arrangement
- basisUnderlying support or principle
- subspaceSubset forming smaller space
- spanDistance between endpoints
- dimensionMeasurable extent or scope
orthogonal · transformation · projection · kernel · range · rank
Distinguishing quality or trait
- spectrumContinuous range of values
- multiplicityState of being many
- spectralGhostlike or wavelength-related
- diagonalizationReducing to diagonal form
determinant · trace · polynomial · root · decomposition · invariant · algebraic · dominant
Reducing to diagonal form
- PCAStatistical dimension reduction
- QRTwo-dimensional scannable code
- factorizationDecomposing into multiplicative parts
- similarityState of being alike
modal · reduction · covariance · symmetric · unitary · truncated
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- ensembleUnified group or outfit
- spacingInterval arrangement between objects
- universalityApplying to all cases
- semicircleHalf a ring
fluctuation · correlation · bulk · edge · asymptotic · localization
State of balance
- linearizationApproximating nonlinear with linear
- attractorConvergence point for systems
- bifurcationDivision into two branches
- fixed-pointElement mapped to itself
perturbation · decay · unstable · asymptotic · transient · steady-state · sensitivity · control
Core significance or position
- PageRankLink-based webpage ordering method
- adjacencyState of being beside
- connectivityState of being linked
- clusteringForming concentrated groups
community · graph · diffusion · modularity · partition · influence · hub · authority
Condition or mode
- wavefunctionQuantum state's mathematical representation
- observableCapable of being detected
- operatorOne who works machinery
- measurementDetermining size or amount
spin · superposition · Dirac · degeneracy · commuting · simultaneous · collapse
Way or method
- resonanceAmplified oscillation at natural frequency
- oscillationRepeated back-and-forth movement
- harmonicOf musical overtones
- structuralRelating to building framework
damping · displacement · amplitude · node · antinode · coupled · mechanical · acoustic
matrix
Ordered numerical arrangement
- basisUnderlying support or principle
- subspaceSubset forming smaller space
- spanDistance between endpoints
dimension · orthogonal · transformation · projection · kernel · range · rank
characteristic
Distinguishing quality or trait
- spectrumContinuous range of values
- multiplicityState of being many
- spectralGhostlike or wavelength-related
diagonalization · determinant · trace · polynomial · root · decomposition · invariant · algebraic · dominant · principal
diagonalization
Reducing to diagonal form
- PCAStatistical dimension reduction
- QRTwo-dimensional scannable code
- factorizationDecomposing into multiplicative parts
similarity · modal · reduction · covariance · symmetric · unitary · truncated
Dyson
Premium vacuum manufacturer
- ensembleUnified group or outfit
- spacingInterval arrangement between objects
- universalityApplying to all cases
semicircle · fluctuation · correlation · bulk · edge · asymptotic · localization
equilibrium
State of balance
- linearizationApproximating nonlinear with linear
- attractorConvergence point for systems
- bifurcationDivision into two branches
fixed-point · perturbation · decay · unstable · asymptotic · transient · steady-state · sensitivity · control
centrality
Core significance or position
- PageRankLink-based webpage ordering method
- adjacencyState of being beside
- connectivityState of being linked
clustering · community · graph · diffusion · modularity · partition · influence · hub · authority · ranking
state
Condition or mode
- wavefunctionQuantum state's mathematical representation
- observableCapable of being detected
- operatorOne who works machinery
measurement · spin · superposition · Dirac · degeneracy · commuting · simultaneous · collapse
mode
Way or method
- resonanceAmplified oscillation at natural frequency
- oscillationRepeated back-and-forth movement
- harmonicOf musical overtones
structural · damping · displacement · amplitude · node · antinode · coupled · mechanical · acoustic
- Engineering Mathcalculus, algebra, linear algebra, differential equations, matrices
- eigenvaluesdiagonalization, multiplicity
- functional analysisnorm, norms, completeness, orthogonality, subspaces
- stochastic processesrandom variable, random variables, martingale, white noise, irreducibility
- operator algebrasprojections, representations, factors, states, ideals
- Spacetime Geometryspacetime, curvature, geodesics, general relativity, manifolds