abstract algebra, a bicomplex number is a pair (w, z) of complex numbers constructed by the Cayley–Dickson process that defines the bicomplex conjugate ( w...
13 KB (1,767 words) - 18:59, 25 April 2024
complex number system, C 2 {\displaystyle \mathbb {C} _{2}} is the bicomplex number system, C 3 {\displaystyle \mathbb {C} _{3}} is the tricomplex number system...
2 KB (489 words) - 21:19, 30 June 2024
In this construction, a bicomplex number (w, z) has conjugate (w, z)* = (w, – z). The biquaternion is then a pair of bicomplex numbers (a, b), where the...
23 KB (3,234 words) - 01:51, 9 May 2024
projective space C P n {\displaystyle \mathbb {CP} ^{n}} by Takeuchi. Bicomplex number Complex geometry CR manifold Dolbeault cohomology Harmonic maps Harmonic...
124 KB (17,658 words) - 01:05, 5 August 2024
numbers (considered as algebras over the reals) leads to four-dimensional bicomplex numbers C ⊗ R C {\displaystyle \mathbb {C} \otimes _{\mathbb {R} }\mathbb...
26 KB (3,143 words) - 02:20, 13 August 2024
split algebras arise in the series bicomplex numbers, biquaternions, and bioctonions, which uses the complex number field C {\displaystyle \mathbb {C}...
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Square (algebra) (category Squares in number theory)
trivial involution to begin the Cayley–Dickson constructions leading to bicomplex, biquaternion, and bioctonion composition algebras. On complex numbers...
15 KB (1,988 words) - 08:16, 5 July 2024
quadratic form z2, then four composition algebras over C are C itself, the bicomplex numbers, the biquaternions (isomorphic to the 2×2 complex matrix ring...
11 KB (1,319 words) - 19:28, 26 June 2024
Diffiety (section Variational bicomplex)
bicomplex. More precisely, any bicomplex determines two spectral sequences: one of the two spectral sequences determined by the variational bicomplex...
26 KB (3,719 words) - 00:49, 28 March 2024
dynamic equations such as the Ginzburg–Landau equation, or by use of a bicomplex variable. A vortex street forms only at a certain range of flow velocities...
22 KB (2,844 words) - 07:11, 22 May 2024
the generation of C by doubling R. When this C is doubled it produces bicomplex numbers, and doubling that produces biquaternions, and doubling again...
14 KB (2,069 words) - 22:59, 28 January 2023
possible to construct Mandelbrot sets in 4 dimensions using quaternions and bicomplex numbers. White and Nylander's formula for the "nth power" of the vector...
10 KB (1,996 words) - 16:19, 9 August 2024
Clifford algebra (redirect from Clifford number)
cases one finds that Cl0(C) ≅ C, the complex numbers Cl1(C) ≅ C ⊕ C, the bicomplex numbers Cl2(C) ≅ M2(C), the biquaternions where Mn(C) denotes the algebra...
64 KB (9,171 words) - 11:01, 7 August 2024
it is well known that[citation needed] jet bundles and the variational bicomplex are the correct domain for such a description. The Hamiltonian variant...
9 KB (1,272 words) - 17:01, 16 April 2024
functor, which can be explicitly computed by the means of the (b, B)-bicomplex. If the field k contains the rational numbers, the definition in terms...
11 KB (1,544 words) - 14:31, 29 May 2024
equation, i.e., for the space of infinite jets) is the so-called variational bicomplex. Furthermore, Vinogradov introduced a new bracket on the graded algebra...
26 KB (2,415 words) - 22:09, 27 May 2024
its motivation. In 1892 Corrado Segre recalled the tessarine algebra as bicomplex numbers. Naturally the subalgebra of real tessarines arose and came to...
15 KB (2,452 words) - 09:07, 7 November 2023
variation Isoperimetric inequality Variational principle Variational bicomplex Fermat's principle Principle of least action Infinite-dimensional optimization...
56 KB (9,263 words) - 19:21, 15 April 2024