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The 28 pages that link to Principal component analysis, each with the reason it gives.

• EigenvalueRelated: Covariance-matrix eigenvalues quantify variance along principal components.

• Euclidean spaceRelated: Its projections and variance calculations use Euclidean lengths and perpendicular directions.

• OrthogonalityRelated: Its component directions are orthogonal eigenvectors of the covariance matrix.

• Singular value decompositionRelated: PCA obtains its principal directions from the right singular vectors of centered data.

• CovarianceRelated: Its covariance-matrix form finds directions that capture the data’s greatest variation.

• Orthogonal projectionRelated: Low-dimensional PCA approximates data by projection onto a principal subspace.

• StandardizationRelated: Standardizing features prevents variables with larger units from dominating its components.

• EigenvectorRelated: Its principal directions are eigenvectors of the data covariance matrix.

• Orthogonal matrixRelated: Its principal directions are orthonormal eigenvectors of a covariance matrix.

• Genetic ancestryRelated: Genetic studies use its components to visualize similarities among sampled populations.

• Gram matrixRelated: The sample Gram matrix enables principal component analysis when features outnumber observations.

• Rank (linear algebra)Related: Its reduced representations can be understood through the effective rank of data matrices.

• Eigenvalue problemRelated: Its principal directions are eigenvectors of the data covariance matrix.

• Spectral theoremRelated: It uses eigenvectors of a covariance matrix to identify principal directions.

• Finite-dimensional vector spaceRelated: Its calculations use finite-dimensional vector spaces to represent observations and directions.

• Diagonal matrixRelated: Diagonalizing a covariance matrix identifies principal directions and their variances.

• Matrix theoryRelated: Its directions arise from eigenvectors or singular vectors of data matrices.

• Multivariate normal distributionRelated: For normal data, uncorrelated principal components are independent.

• Michael E. MannRelated: The 1998 study used this method to summarize regional tree-ring networks.

• Eigenvalues and eigenvectorsRelated: Eigenvectors of the covariance matrix give the principal directions; eigenvalues measure their variances.

• ChemometricsRelated: It compresses spectra and other high-dimensional chemical measurements while revealing dominant patterns.

• Kosambi–Karhunen–Loève theoremRelated: The theorem extends variance-ranked orthogonal decomposition from finite data vectors to random processes.

• Sample mean and covarianceRelated: The sample covariance matrix supplies the directions and variances used in its standard formulation.