Revision #617 → #1448 · back to history
addedOrthogonal group O(n)56e0023a73d0
addedSpecial orthogonal group SO(n)7229726c2592
addedOrthogonal matrix over a field F7216e0fb22fb
addedOrthogonal group of a form70ecffc1119e
addedOrthogonal groups are algebraic groupsba47abc7bed2
addedCharacterization of orthogonal group elements20be281bd3e3
addedO(n) as norm-preserving endomorphismsaf0255933fea
addedEuclidean isometry group E(n)c63b023fe79f
addedPoint stabilizer isomorphic to O(n)2022d9d658c2
addedHomomorphism p from E(n) to O(n)ba03dc692ad5
addedp is a well-defined homomorphismdf077151c9a0
addedKernel of p is the translationsc20b15c6a2cf
addedEuclidean group is a semidirect product286ec7aff70c
addedO(n) as orthogonal matrices20fa000d1918
addedDeterminant of orthogonal matrix is ±14ce053ba206a
addedSpecial orthogonal group (determinant 1)0a64534ffb86
addedSO(n) is a normal subgroup of O(n)62a0faf1fba9
added{±I} is a characteristic subgroup799d20726e6f
addedSO(2) is abelian2c5eecfd8ed1
addedCanonical form of orthogonal matricesc07979e29deb
addedMembership in SO(n) via −1 countcc6ef58bf0fd
addedEuler's rotation theoremd53679916460
addedReflections in O(n)2c7477ae8405
addedRotation as product of two reflectionsff635a1b75d6
addedReflections generate O(n)7cf266d2bff4
addedCartan–Dieudonné theoremf64672bfc841
addedReflection through the origina0fc598ab617
addedO(n) is symmetry group of the sphereaf1d6f6a789b
addedSO(2) isomorphic to circle group0ebe219d0889
addedO(n), SO(n) are compact Lie groups35020d703974
addedO(n) defined by n(n+1)/2 equations76b11c86d326
addedO(n) has two irreducible componentscbc0427d4b4a
addedMaximal torus in a compact Lie group5c8240e40ca1
addedForm of maximal tori in O(2n), SO(2n)08d66ef527cb
addedWeyl group of SO(2n+1)4394f8792943
addedWeyl group of SO(2n)34c99234edb8
addedLow-dimensional orthogonal groups2d7f4f2a05f8
addedFundamental group of SO(n)95a5fee4235b
addedStable orthogonal groupf2a7eba3adc2
addedSphere as homogeneous space for O(n+1)f181cb26ccf5
addedStabilization of homotopy groups34267b2aea32
addedBott periodicity for O2180c7dcf08e
addedHomotopy groups as stable vector bundles1c121065aa21
addedπ0(O) from orientation5a1a35754836
addedπ1(O) is spinb0a15b11a453
addedπ2(O) vanishesbbeaaeb940ed
addedGeneral Lie group homotopy factsc34d1deb11dd
addedπ0(KO) is the dimension950764ec3def
addedKO generators from division algebrasbde147702b7c
addedMaslov index interpretation23815e06861c
addedWhitehead tower of Oe4bdd007fd49
addedSylvester's law of inertiaeff7e9500123
addedIndefinite orthogonal group O(p,q)3becd504efa0
addedO(p,q) = O(q,p)8f4adf2d8199
addedO(p,q) has four connected components4961f08c0a3c
addedO(3,1) is the Lorentz group195ce90b22d0
addedClassification of complex quadratic formse034a081901b
addedComplex orthogonal group O(n,C)dca4dbd5755c
addedO(n,C) has two connected componentscdbda8328417
addedO(n,C), SO(n,C) as complex Lie groupsacdec1f614a3
addedEquivalence of quadratic forms via congruence47af6f15ea48
addedClassification over finite fields3330ab53c449
addedWitt's decomposition theorema6260a42281b
addedChevalley–Warning theoreme8129b438183
addedOne orthogonal group O(2n+1,q) in odd dimensionbf916ff78dba
addedTwo orthogonal groups in even dimension4411898a7c19
addedO^ε(2,q) is a dihedral group143574eff9c6
addedMap (a,b)↦a+αb is a homomorphism05ffadafc81c
addedImage in O+(2n,q) is cyclic of order qb3f07bf0884f
addedO−(2n,q) and (q+1)-roots of unity98fdb037dcce
addedOrders of orthogonal groups in odd characteristic45ff530d4ecd
addedOrder formulas in characteristic two3752f4ddee3b
addedDickson invariantcbbda891359d
addedAlgebraic definition of Dickson invariant47232d3916a6
addedSO is kernel of Dickson invariantd505f5316099
addedOrthogonal groups generated by reflections3265ab0f76c4
addedReflection in characteristic twoc07342b16c92
addedCenter has order 1 in characteristic 2df015dc21d6f
addedOdd-dimensional char 2 equals symplectic groups4c1889d33fa6
addedEven-dimensional char 2 subgroup of symplectice57880054422
addedSpinor norm74726e0c4e62
addedSpinor norm trivial over the reals116bf01820ba
addedQuadratic forms as torsors of orthogonal group67ad699b130a
addedSpin covering short exact sequence708a7d8bd928
addedConnecting homomorphism is the spinor norm397a10b267f3
addedOrthogonal Lie algebra3a6ba81609e6
addedSpecial orthogonal Lie algebra of a form0be6c24026c3
addedEight inclusions and Bott periodicitydad4230422e0
addedUnitary subgroup U(n) of O(2n)ba557ce64186
addedOrthogonal transforms are conformalb709bfec22aa
addedConformal orthogonal group CO(n)c88fba065e2d
addedDiscrete subgroups are finite (point groups)206ce69d17bc
added2D finite subgroups cyclic or dihedrala7f51c34c3c7
addedPermutation and signed permutation matricesedab4e4a4e09
addedPin groups and PO(n)a879b13a6803
addedSpin group and PSO(n)7c60fb5140aa
addedCover multiplicities of Spin and PSO30085ab7e158
addedStiefel manifold as principal homogeneous space71ec98099c4a
addedIncomplete Stiefel manifolds are not principal65cab5df27a6