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Diff — Singular value decomposition

Revision #3489 → #4031 · back to history

modifiedSVD related to polar decomposition27b91965e78b
FieldFrom #3489To #4031
notePolar decomposition of operators/matrices is not present in Mathlib (loogle for "polarDecomposition" returns 0 hits), so its relation to the SVD is not formalized.Polar decomposition of operators/matrices is not present in Mathlib, so its relation to the SVD is not formalized.
modifiedHouseholder reflection38e1ad47709f
FieldFrom #3489To #4031
noteHouseholder reflections/transformations are not formalized as a named construction (loogle for "Householder" returns 0 hits).Householder reflections/transformations are not formalized as a named construction.
modifiedPauli matricesd78d3095627e
FieldFrom #3489To #4031
noteThe Pauli matrices are not defined as named constants in Mathlib (loogle for "Pauli" returns 0 hits).The Pauli matrices are not defined as named constants in Mathlib.
modifiedPartial isometry504b56193a9b
FieldFrom #3489To #4031
notePartial isometries on Hilbert spaces are not a named concept in Mathlib (loogle for "partialIsometry" returns 0 hits).Partial isometries on Hilbert spaces are not a named concept in Mathlib.
addedEigenvalue decomposition12c98bf34281
addedBest low-rank approximation via truncated SVDae6130b77813
addedFrobenius norm equals sum of squared singular values55336e836f74
addedNearest orthogonal via polar decomposition unitary factor715599fe69db
addedSchmidt decomposition853d4288260d
addedRayleigh quotient378f7700e286
addedOrthonormal basis3ab6e03e6f63
addedRank of a matrix23ded3da830f
addedRange of a linear map904bfa42ca71
addedHermitian matrixf8b33abbe0b5
addedUnit sphere35a71612a7f6
addedBounded operator21a5eb2457c0