Revision #663 → #1582 · back to history
addedSplit-complex number54617abded13
addedAddition and multiplicationc2570a1f2900
addedMultiplication is commutative, associative, distributive41227beb13d6
addedSplit-complex conjugate0f816454b711
addedConjugate is an involutionfc9d2950a680
addedSquared modulus0f0c6440c675
addedComposition algebra property of modulus9d5e8cc1022c
addedModulus has signature (1,-1)ce9f2d0415da
addedAssociated bilinear form302822b246f2
addedInvertibility and multiplicative inverse8ebcde9a4040
addedTwo nontrivial null idempotents061b88a7368d
addedRepresentation in the null basis017a316191d3
addedArithmetic in the diagonal basise51ec1e13b55
addedConjugate and modulus in diagonal basisd4bc436fdad3
addedRing isomorphism to direct sum of reals3004fe213e7f
addedHyperbolas correspond under the mappingbeca196dc5bc
addedHyperbolic versor as squeeze mapping9f655cac4419
addedIsomorphism is rotation by 45° and dilation by √277ac9fe5ac51
added(1+1)-dimensional Minkowski spacee3c06cd8b2e5
addedLevel set is a hyperbolade4e90f6755d
addedUnit hyperbola2bc678e9d89f
addedConjugate hyperbola721c08d52921
addedNull cone asymptotes63b665ef3f4d
addedHyperbolic-orthogonalitydcb9be52a04e
addedSplit-complex Euler's formula769e2d176530
addedHyperbolic versor has norm 1c4a4d353df17
addedMultiplication by λ is a hyperbolic rotation82e76d86cf60
addedGeneralized orthogonal group O(1,1)2746f96098e2
addedExponential map is a group isomorphismf093c20a14ad
addedPolar decomposition off the diagonalsd15721d33c05
addedQuotient of polynomial ring presentation5139b9390e25
addedCommutative algebra over the realse9529c6818c0
addedNot a field; null elements not invertiblee3c7d0c16f33
addedNonzero null elements are zero divisors134919fd18c5
addedTopological ring31ce2aa55948
addedComposition algebra8cac1b655db7
addedIsomorphic to group ring of C21b85f643531d
addedIdentity component elements have four square roots9a4c5b17d4ad
addedIdempotents are their own square roots1a64feb84e64
addedMatrix representation by I and Je97405b6dbaa
addedStandard 2×2 matrix representationb3c0b8e68e37
addedGeneral trace-zero det -1 matrix; determinant equals modulus6b7ea8701974
addedDirac matrix representation58e4c556db16
addedFuture quadrant polar decomposition03abbbaefa86
addedAdditivity of rapiditiesfd5911829c6a
addedCanonical events are hyperbolic-orthogonalc422f69dbf73
addedNine-point hyperbola3724df149b7b