In algebra, a split-complex number (or hyperbolic number, also perplex number, double number) is based on a hyperbolic unit j satisfying j 2 = 1 {\displaystyle...

angle in the split-complex plane correspond to angle in Euclidean geometry. Indeed, they each arise in polar decomposition of a complex number z. Hyperbolic...

apart was illegitimate. (See Mathematical fallacy.) −1 Dual number Split-complex number j is usually used in engineering contexts where i has other meanings...

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary...

subalgebras isomorphic to the split-complex number plane. Furthermore, just as the quaternion algebra H can be viewed as a union of complex planes, so the hyperbolic...

{\displaystyle j} of the split-complex numbers, and therefore the multicomplex numbers contain a number of copies of the split-complex number plane. With respect...

arguments and values in the split-complex number plane, much as functions of a complex variable involve ordinary complex numbers. William Kingdon Clifford...

fortress complex built at the end of the third century AD by the Roman Emperor Diocletian as his retirement residence. About half of the complex was for...

Klein four-group. In a similar fashion, the group of units of the split-complex number ring, when divided by its identity component, also results in the...

proper time rapidity relativistic wave equations relativistic mass split-complex number unit hyperbola world line black holes no-hair theorem Hawking radiation...

between the three planar number systems (complex, dual and split-complex numbers) and the three non-Euclidean geometries. The number system that corresponds...

z=\left(\tan {\frac {\theta }{2}}\right)(\cosh s+j\sinh s)} is the split-complex number: 118  for a line in the Lobachevski plane. Since there are lines...

arises through Euler's formula in the complex plane. Other one-parameter groups occur in the split-complex number plane as the unit hyperbola { exp ⁡ (...

determinant is negative only arises in a plane with ε2 =+1, that is a split-complex number plane. Only one quarter of this plane is the image of the exponential...

n\times n} complex unitary matrix. spectrum Set of the eigenvalues of a matrix. split-complex number An element of a split-complex plane split-complex plane...

Split Saint Jerome Airport (Croatian: Zračna luka Sveti Jeronim Split; IATA: SPU, ICAO: LDSP), also known as Split Airport (Croatian: Zračna luka Split)...

map, that is, exp ⁡ ( v ) = v {\displaystyle \exp(v)=v} . In the split-complex number plane z = x + y ȷ , ȷ 2 = + 1 , {\displaystyle z=x+y\jmath ,\quad...

must use the split forms (of maximally indefinite index), as the group SO is compact. Compact Lie algebra Real form Split-complex number Split orthogonal...

only 2-dimensional hypercomplex algebra that is a field. Split algebras such as the split-complex numbers that include non-real roots of 1 also contain idempotents...

every complex semisimple Lie algebra g has a split real form, which is unique up to isomorphism. It has maximal index among all real forms. The split form...

In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton...

In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite...

traffic forecasting problems. Pfister's sixteen-square identity Split-complex number PG(3,2) "Ensembles de nombre" (PDF) (in French). Forum Futura-Science...

mapping called a Lorentz boost. This insight follows from a study of split-complex number multiplications and the diagonal basis which corresponds to the pair...

Split (/splɪt/, Croatian: [splît] ), historically known as Spalato (Italian: [ˈspaːlato]; Venetian: Spàlato; see other names), is the second-largest city...

He saw the modelling power of hyperbolic versors operating on the split-complex number plane, and in 1891 he introduced hyperbolic quaternions to extend...

Whereas the unit circle is associated with complex numbers, the unit hyperbola is key to the split-complex number plane consisting of z = x + yj, where j...

multiplication by a complex number of modulus 1 acts as a rotation. The complex plane is sometimes called the Argand plane or Gauss plane. In complex analysis,...

an area code overlay complex is a telephone numbering plan that assigns multiple area codes to the same geographic numbering plan area (NPA). Area code...

Jerusalem and the First Council of Nicaea. Historiography of the split is complicated by a number of factors, including a diverse and syncretic range of religious...