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- Split-complex_number abstract "In abstract algebra, the split-complex numbers (or hyperbolic numbers, also perplex numbers) are a two-dimensional commutative algebra over the real numbers different from the complex numbers. Every split-complex number has the form x + y j,where x and y are real numbers. The number j is similar to the imaginary unit i, except that j2 = +1.As an algebra over the reals, the split-complex numbers are the same as the direct sum of algebras R ⊕ R (under the isomorphism sending x + y j to (x + y, x − y)). The name split comes from this characterization: as a real algebra, the split-complex numbers split into the direct sum R ⊕ R.Geometrically, split-complex numbers are related to the modulus (x2 − y2) in the same way that complex numbers are related to the square of the Euclidean norm (x2 + y2). Unlike the complex numbers, the split-complex numbers contain nontrivial idempotents (other than 0 and 1), as well as zero divisors, and therefore they do not form a field.In interval analysis, a split complex number x + y j represents an interval with midpoint x and radius y. Another application involves using split-complex numbers, dual numbers, and ordinary complex numbers, to interpret a 2 × 2 real matrix as a complex number.Split-complex numbers have many other names; see the synonyms section below. See the article Motor variable for functions of a split-complex number.".
- Split-complex_number thumbnail Drini-conjugatehyperbolas.svg?width=300.
- Split-complex_number wikiPageExternalLink 9311032v2.pdf.
- Split-complex_number wikiPageExternalLink HYP2.PDF.
- Split-complex_number wikiPageExternalLink 1.14605.
- Split-complex_number wikiPageExternalLink warmus.pdf.
- Split-complex_number wikiPageID "893559".
- Split-complex_number wikiPageRevisionID "595822744".
- Split-complex_number hasPhotoCollection Split-complex_number.
- Split-complex_number subject Category:Hypercomplex_numbers.
- Split-complex_number subject Category:Linear_algebra.
- Split-complex_number type Abstraction100002137.
- Split-complex_number type Amount105107765.
- Split-complex_number type Attribute100024264.
- Split-complex_number type HypercomplexNumbers.
- Split-complex_number type Magnitude105090441.
- Split-complex_number type Number105121418.
- Split-complex_number type Property104916342.
- Split-complex_number comment "In abstract algebra, the split-complex numbers (or hyperbolic numbers, also perplex numbers) are a two-dimensional commutative algebra over the real numbers different from the complex numbers. Every split-complex number has the form x + y j,where x and y are real numbers.".
- Split-complex_number label "Binäre Zahl".
- Split-complex_number label "Liczby podwójne".
- Split-complex_number label "Nombre complexe déployé".
- Split-complex_number label "Numero complesso iperbolico".
- Split-complex_number label "Número complexo hiperbólico".
- Split-complex_number label "Split-complex number".
- Split-complex_number label "Двойные числа".
- Split-complex_number label "عدد عقدي مقسم".
- Split-complex_number label "分解型複素数".
- Split-complex_number label "雙曲複數".
- Split-complex_number sameAs Dvojné_číslo_(matematika).
- Split-complex_number sameAs Binäre_Zahl.
- Split-complex_number sameAs Nombre_complexe_déployé.
- Split-complex_number sameAs Numero_complesso_iperbolico.
- Split-complex_number sameAs 分解型複素数.
- Split-complex_number sameAs 분할복소수.
- Split-complex_number sameAs Liczby_podwójne.
- Split-complex_number sameAs Número_complexo_hiperbólico.
- Split-complex_number sameAs m.03mglq.
- Split-complex_number sameAs Q864145.
- Split-complex_number sameAs Q864145.
- Split-complex_number sameAs Split-complex_number.
- Split-complex_number wasDerivedFrom Split-complex_number?oldid=595822744.
- Split-complex_number depiction Drini-conjugatehyperbolas.svg.
- Split-complex_number isPrimaryTopicOf Split-complex_number.
