Revision #658 → #1571 · back to history
addedSingular value decomposition1698cfb8a4a0
addedFormal SVD factorization74590faee3d0
addedExistence of SVD4809852da6f0
addedSingular values31cc1c027e38
addedNumber of nonzero singular values equals rank9fd4a00d8bcb
addedLeft- and right-singular vectors3fd4fac0a448
addedSingular values orderable, Sigma uniquely determined05112f6916b6
addedCompact SVDaa9a9c3fb97b
addedSVD as composition of three geometric transformations92e953329ed8
addedReflections determined by sign of determinantd17cae28ac0d
addedSingular values as ellipse/ellipsoid semiaxes20ce58eee257
addedColumns of U and V form orthonormal bases65e53abdf786
addedPositive-semidefinite Hermitian case1839499980a2
addedFirst columns of U span the column spacec1d137c666ef
addedLast columns of U span the cokernelda3bf43a3486
addedFirst columns of V span the row spacede39705d9b98
addedLast columns of V span the null space688bea7a16be
addedGeometric content of the SVD theoremccf48168cd7f
addedWorked SVD of a 4x5 matrix79874bacfe67
addedNon-uniqueness of the SVDc159d3ede351
addedCompact SVD of the example matrixb11f5664cc96
addedSingular value characterization334a9e4aea6f
addedLeft- and right-singular vectors3fcea329f294
addedDiagonal entries equal singular values697a97a965a0
addedDegenerate singular value86ff3e9c49e9
addedSingular vectors of singular value zero4d729e148590
addedUniqueness for non-degenerate singular valuesb845edeb6f4a
addedSVD relations to eigendecomposition91f814fc1b4b
addedNormal matrix case via spectral theorem026c1c89055b
addedConnection via polar decomposition theoremf3e8a79841b6
addedEvery matrix has an SVD648c9042a895
addedPseudoinverse via SVDdc73b4fb03d8
addedNull vector as right-singular vector for zero singular value96a9d7042133
addedLeft null vector04e82ccf33ba
addedTotal least squares solution3e8e6c1090a4
addedSingular vectors span null space and rangea9d53d80470b
addedRank equals number of nonzero singular values2c48e2e2ffe2
addedEckart–Young theorema29c2855688f
addedSVD image compression0be922589da9
addedSeparable matrix3435c8a52a87
addedIndex of separability87f89cbc1e83
addedNearest orthogonal matrix via SVD7b367a65fd43
addedOrthogonal Procrustes problemae35e2e4d297
addedKabsch algorithmc2fa1e56b414
addedPrincipal components from SVD4de9243dccf0
addedCondition number3aaae71425a9
addedEntanglement criterion via Schmidt decomposition7ccd18aaf27a
addedLargest eigenvalue as maximum of Rayleigh quotiente4ac25a1cf43
addedSpectral theorem yields unitary diagonalizationf5c5750d5de0
addedSingular values as maxima over subspaces101459c07c0f
addedLeft and right-singular vectors statement4cf29b04ca1c
addedOne-sided Jacobi algorithm66f9fa3a707e
addedTwo-sided Jacobi algorithm72f56b0ffa55
addedSingular vectors as eigenvectors of M*M and MM*b2a56d3aebbc
addedAnalytic 2x2 SVDe4d74007489b
addedThin SVDf47428e198b1
addedCompact SVDe9abdcc171a6
addedTruncated SVDd8941f38ae04
addedKy Fan k-norm30f5cd85a14f
addedKy Fan 1-norm equals operator normb7aafdb80a1f
addedTrace (nuclear) normc28effee64ad
addedHilbert–Schmidt inner product96f6fcf82e42
addedFrobenius normfe3b5eb51677
addedInvariance of singular values under unitary transforms28888bd2d460
addedScale-invariant SVD0b6ef2704cc9
addedSVD for bounded operators on Hilbert spaces8538d5c5330b
addedSingular values of compact operatorsb08519fbccf7
addedCompactness equivalence theorem7083cfe30fd4