Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Split-complex_number> ?p ?o }
- Split-complex_number abstract "In abstract algebra, the split-complex numbers (or hyperbolic numbers, also perplex numbers, and double 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 j 2 = +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. It arises, for example, as the real subalgebra generated by an involutory matrix.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 1up.
- Split-complex_number wikiPageExternalLink HYP2.PDF.
- Split-complex_number wikiPageExternalLink generalized_complex_numbers.pdf.
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- Split-complex_number wikiPageWikiLink 2_×_2_real_matrices.
- Split-complex_number wikiPageWikiLink Abstract_algebra.
- Split-complex_number wikiPageWikiLink Academic_Press.
- Split-complex_number wikiPageWikiLink Addition.
- Split-complex_number wikiPageWikiLink Algebra_over_a_field.
- Split-complex_number wikiPageWikiLink Area.
- Split-complex_number wikiPageWikiLink Argentina.
- Split-complex_number wikiPageWikiLink Associative.
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- Split-complex_number wikiPageWikiLink Asymptote.
- Split-complex_number wikiPageWikiLink Automorphism.
- Split-complex_number wikiPageWikiLink Basis_(linear_algebra).
- Split-complex_number wikiPageWikiLink Bicomplex_number.
- Split-complex_number wikiPageWikiLink Bilinear_form.
- Split-complex_number wikiPageWikiLink Biodiversity_Heritage_Library.
- Split-complex_number wikiPageWikiLink Birkhäuser.
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- Split-complex_number wikiPageWikiLink Cartesian_coordinate_system.
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- Split-complex_number wikiPageWikiLink Category:Hypercomplex_numbers.
- Split-complex_number wikiPageWikiLink Category:Linear_algebra.
- Split-complex_number wikiPageWikiLink Category_of_rings.
- Split-complex_number wikiPageWikiLink Cayley–Dickson_construction.
- Split-complex_number wikiPageWikiLink Characteristic_(algebra).
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- Split-complex_number wikiPageWikiLink Circle_group.
- Split-complex_number wikiPageWikiLink Clifford_algebra.
- Split-complex_number wikiPageWikiLink Clifford_biquaternion.
- Split-complex_number wikiPageWikiLink College_Mathematics_Journal.
- Split-complex_number wikiPageWikiLink Commutative.
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- Split-complex_number wikiPageWikiLink Commutative_ring.
- Split-complex_number wikiPageWikiLink Commutativity.
- Split-complex_number wikiPageWikiLink Complex_analysis.
- Split-complex_number wikiPageWikiLink Complex_number.
- Split-complex_number wikiPageWikiLink Complex_numbers.
- Split-complex_number wikiPageWikiLink Complex_variable.
- Split-complex_number wikiPageWikiLink Composition_algebra.
- Split-complex_number wikiPageWikiLink Cyclic_group.
- Split-complex_number wikiPageWikiLink D._H._Lehmer.
- Split-complex_number wikiPageWikiLink David_Mermin.
- Split-complex_number wikiPageWikiLink Definite_bilinear_form.
- Split-complex_number wikiPageWikiLink Definite_quadratic_form.
- Split-complex_number wikiPageWikiLink Derrick_Henry_Lehmer.
- Split-complex_number wikiPageWikiLink Determinant.
- Split-complex_number wikiPageWikiLink Dilation_(metric_space).
- Split-complex_number wikiPageWikiLink Direct_sum_of_modules.
- Split-complex_number wikiPageWikiLink Discrete_mathematics.
- Split-complex_number wikiPageWikiLink Distributive_property.
- Split-complex_number wikiPageWikiLink Division_algebra.
- Split-complex_number wikiPageWikiLink Dual_number.
- Split-complex_number wikiPageWikiLink Elsevier.
- Split-complex_number wikiPageWikiLink Encyclopaedia_of_Mathematics.
- Split-complex_number wikiPageWikiLink Encyclopedia_of_Mathematics.
- Split-complex_number wikiPageWikiLink Euclidean_norm.
- Split-complex_number wikiPageWikiLink Eulers_formula.
- Split-complex_number wikiPageWikiLink Even_subalgebra.
- Split-complex_number wikiPageWikiLink Field_(mathematics).
- Split-complex_number wikiPageWikiLink Frame_of_reference.
- Split-complex_number wikiPageWikiLink Generalized_orthogonal_group.
- Split-complex_number wikiPageWikiLink Generator_(mathematics).
- Split-complex_number wikiPageWikiLink Geometry.
- Split-complex_number wikiPageWikiLink Group_(mathematics).
- Split-complex_number wikiPageWikiLink Group_action.
- Split-complex_number wikiPageWikiLink Group_isomorphism.
- Split-complex_number wikiPageWikiLink Group_ring.
- Split-complex_number wikiPageWikiLink Hyperbola.
- Split-complex_number wikiPageWikiLink Hyperbolic-orthogonal.
- Split-complex_number wikiPageWikiLink Hyperbolic_angle.
- Split-complex_number wikiPageWikiLink Hyperbolic_cosine.
- Split-complex_number wikiPageWikiLink Hyperbolic_function.
- Split-complex_number wikiPageWikiLink Hyperbolic_orthogonality.
- Split-complex_number wikiPageWikiLink Hyperbolic_sector.
- Split-complex_number wikiPageWikiLink Hyperbolic_sine.
- Split-complex_number wikiPageWikiLink Hypercomplex_number.
- Split-complex_number wikiPageWikiLink Ideal_(ring_theory).
- Split-complex_number wikiPageWikiLink Idempotence.
- Split-complex_number wikiPageWikiLink Idempotent.
- Split-complex_number wikiPageWikiLink Idempotent_element.
- Split-complex_number wikiPageWikiLink If_and_only_if.
- Split-complex_number wikiPageWikiLink Imaginary_unit.
- Split-complex_number wikiPageWikiLink Indefinite_orthogonal_group.
- Split-complex_number wikiPageWikiLink Inner_product.
- Split-complex_number wikiPageWikiLink Inner_product_space.
- Split-complex_number wikiPageWikiLink International_Journal_of_Theoretical_Physics.
- Split-complex_number wikiPageWikiLink Interval_analysis.
- Split-complex_number wikiPageWikiLink Interval_arithmetic.