Revision #903 → #1520 · back to history
addedQuaternion6fa58f62269e
addedZero quaterniona3b36d60a4e3
addedScalar and vector parts of a quaternionea15fb979f6d
addedScalar quaternionccaca97d2ed1
addedVector quaternion83d841c7545b
addedQuaternions as a 4-dimensional vector space8875f39fbb62
addedHamilton product30cc010a21ba
addedQuaternions form a division algebrabf2efed52bdc
addedMultiplication of basis elements by 1c434105bb852
addedProducts of basis elements i, j, k726025d2056e
addedCenter of a noncommutative ringcdab202859cd
addedCenter of the quaternion algebra18177bc35918
addedEquation z^2 + 1 = 0 over quaternions98e379170f2a
addedHamilton product expansionb5b124fa5a68
addedScalar quaternion (restated)46669b4a114d
addedVector quaternion (restated)50b3667fab0b
addedScalar part and vector part3f7caa821eff
addedConjugate of a quaternion9aae9fa2d4fe
addedConjugation is an involutionbc85c8dfed21
addedConjugate of a product reverses orderdec2db3840ad
addedExtracting scalar and vector parts via conjugation06af08e97a5c
addedNorm of a quaternion42ef6682c446
addedNorm scales by absolute value of real scalar3252901f8f91
addedNorm is multiplicative85d89787da50
addedDistance between quaternions0d550a505d7e
addedQuaternions form a metric spaceb1c1ab86322d
addedUnit quaternion and versorfa791764d0f6
addedPolar decomposition of nonzero quaternion494035403c8b
addedReciprocal of a quaternion2bc9edb2127c
addedQuaternions form a non-commutative associative algebra8dd2e844b22d
addedFrobenius theorem1fd07009a68f
addedHurwitz's theorembe02f9e32273
addedQuaternion group Q_89ab9a89cadb5
addedQuaternions as quotient of real group ring of Q_87542229c2b31
addedDot product of vector quaternionse68b1ea24d2b
addedCross product of vector quaternionsa857ab3b6d9b
addedCommutator of vector quaternionsbcba7b735d98
addedCommutativity criterion via collinearity53409bc87e7d
addedUnit quaternions identified with rotations2724c8948094
addedRepresentation as complex 2x2 matrices36ab1a9a5d00
addedProperties of complex 2x2 representationfe158304d935
addedRepresentation as real 4x4 matrices5903bcd28a64
added48 distinct real 4x4 representationsa54a4cc595f2
addedLagrange's four-square theorem9f4406accf1b
addedQuaternions via Cayley–Dickson constructionf200a79b4469
addedSquare roots of -1 form the unit sphere1f46b4ca12af
addedOnly negative real quaternions have infinitely many square rootsce49bb86bf18
addedComplex plane embedded via square root of -1a0309d6741ac
addedSubalgebra generated by non-real quaternion911d40ce1a1a
addedCommutative subrings of the quaternion ring5694ec81139c
addedExistence of square roots of arbitrary quaternions46d5d4f46e33
addedNumber of square roots by quaternion type57df117e6fb5
addedExponential of a quaternion08de3d09cd08
addedLogarithm of a quaternion43a15dd9591a
addedPolar decomposition of a quaternion952e1e28bb3e
addedPolar form of a unit quaternion31cc9b7a8762
addedPower of a quaternion1e93d3b1ab8e
addedGeodesic distance between unit quaternions3cc9ab869550
addedConjugation by unit quaternion as rotation529fe02b814e
addedUnit quaternions double cover SO(3)36d8bac1f7b6
addedVersors' group isomorphic to SU(2)350728ab4d4f
addedRing of Hurwitz quaternionsf2449caf7ded
addedQuaternion algebra over a field3c6052824d69
addedClassification of quaternion algebras454796f70f6c
addedReflection formula in Cl_{3,0}a7466dc1aa2c
addedIsomorphism between quaternions and even Cl_{3,0}4e5ac43842ec
addedBrauer group of the reals0de941477218
addedArtin–Wedderburn theorem (Wedderburn's part)acb30bff2240