Revision #882 → #1462 · back to history
addedPauli matrices97ef4897fd09
addedPauli matrices form a basis of 2x2 Hermitian matricese4a4c3fd3ddc
addedPauli product relation6aee8f8f63f9
addedPauli matrices generate su(2) and Clifford algebra80cc5b662c48
addedCompact expression for Pauli matrices3c0f78479c32
addedPauli matrices are involutory71777a66f1fe
addedDeterminants and traces of Pauli matrices6fa1b33c5de0
addedEigenvalues of Pauli matrices94d2da18995f
addedPauli matrices with identity form orthogonal basisde95d8130638
addedCommutation relationsf02e046ed1ca
addedAnticommutation relationsf09abcb24fdf
addedPauli matrices as Clifford algebra generators1f0cdb815be2
addedEigenvalues and eigenvectors of Pauli matrices5183b30038ae
addedPauli vectordfe65823243c
addedPauli vector mapping mechanism6a0bd0b59814
addedMap to traceless Hermitian matrices is Lie algebra isomorphismc725f6909e4c
addedPauli vector as Hermitian traceless dual vector9df611804ba7
addedCompleteness relation for Pauli vector componentsdd9ceee34faa
addedNorm given by determinant29a745d24347
addedConjugation action preserves Hermitian traceless and normdcf8440aaf64
addedDouble cover of SO(3) by SU(2)849ac9339d0a
addedCross-product via matrix commutator56e4986b325d
addedEigenvalues of Pauli vectorefddc22d1d5c
addedPauli vector diagonalizable via polynomial factorisationd2e369e37f1b
addedNormalized eigenvectors of Pauli vectore713365d7d8d
addedEigenvectors in spherical coordinatesf0ba0f208d44
addedPauli 4-vector455390c4d7ef
addedMap encodes Minkowski metric in determinant3195f112d091
addedSecond Pauli 4-vector12dc87242654
addedSL(2,C) acts as isometries on Minkowski spacef584dd83ac4d
addedTrace identity for 2x2 matrices3b9c9652b168
addedSum of commutator and anticommutator0cf2e9fcd3df
addedContraction with two 3-vectorseb5aee5a650d
addedIndex translation to dot and cross product2783e4977e87
addedGeometric algebra interpretation with pseudoscalar247ee62b48cf
addedSpin operator commutation relation899e1074083e
addedTrace relations from commutation/anticommutation234bba34cea4
addedExtended trace relations including identityc0b18dc62862
addedEven powers of Pauli vectord96cbfbf9589
addedOdd powers of Pauli vectorcd82194ea39d
addedMatrix exponential via Taylor seriesb35c87dcc449
addedExponential analog to Euler's formulad3576476bd11
addedDeterminant of exponential is 1d9d7cae6bd6a
addedSylvester's formula generalizationf40c551a1747
addedSU(2) group composition law5a6b3e096a7b
addedSpherical law of cosines for composition18fcddd7ebce
addedBCH expansion composite rotation parameters8bd91cc9978a
addedAdjoint action on Pauli vector6fc3ee2d69d7
addedSingle qubit operator under rotationc81cc48dde16
addedCompleteness relation in index notationf855ff47e694
addedExpansion of 2x2 complex matrixcab033040690
addedAlternative completeness relation with sigma_0922923c2c6e4
addedBloch sphere representation of density matrix04c4789128f5
addedPure state idempotent density matrix8632ccc6a409
addedTransposition (permutation) operatorda56eeeed397
addedDirac's spin exchange operator form2377e3faa694
addedEigenvalues of permutation operatord9ea6bf0ed34
addedSU(2) and its Lie algebra6694597c2c1e
addediσ_j as infinitesimal generators of SU(2)11e75d36a330
addedCartan decomposition of SU(2) is trivialbabf1fdb8bc5
addedsu(2) isomorphic to so(3); SU(2) double covers SO(3)fd8e9b7fe6b9
addedSpan isomorphic to quaternions2d5b38af4b1f
addedAlternative isomorphism in reversed order1a16357235ea
addedVersors form group isomorphic to SU(2)a785a1925c98
addedCayley-Klein position matrix191019d3c740
addedRotation transformation matrix257708212d2d
addedPauli matrices as spin angular momentum operatorsf1edc8d94ed5
addedSpin-1/2 particles require 4π rotationcda4b39bb32e
addedSpin operator as fundamental representation of SU(2)b5a5754021f9
addedGeneral Pauli group6fcf4abc372d
addedRelativistic Sigma matricese7f8bcd6fd08
addedSigma matrices share algebraic properties of Pauli matrices7e16645dc86f
addedLorentz generators Σ μν on spinorse425037f8a49
addedDirac α_k matrices6b7dca525609
addedΣ μν in terms of gamma matrix commutator7c6bd80dc9fc
addedPauli matrices as single-qubit gates90fdf353bc0c