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In mathematics, hypercomplex analysis is the extension of real analysis and complex analysis to the study of functions where the argument is a hypercomplex number. The first instance is functions of a quaternion variable, where the argument is a quaternion. A second instance involves functions of a motor variable where arguments are split-complex numbers. In mathematical physics, there are hypercomplex systems called Clifford algebras. The study of functions with arguments from a Clifford algebra is called Clifford analysis.

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rdfs:label	Hypercomplex analysis (en)
rdfs:comment	In mathematics, hypercomplex analysis is the extension of real analysis and complex analysis to the study of functions where the argument is a hypercomplex number. The first instance is functions of a quaternion variable, where the argument is a quaternion. A second instance involves functions of a motor variable where arguments are split-complex numbers. In mathematical physics, there are hypercomplex systems called Clifford algebras. The study of functions with arguments from a Clifford algebra is called Clifford analysis. (en)
sameAs	Hypercomplex analysis Hypercomplex analysis
dbp:wikiPageUsesTemplate	dbt:ISBN dbt:Reflist
Subject	Functions and mappings Hypercomplex numbers Mathematical analysis
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Hypercomplex_analysis?oldid=1039619536&ns=0
Wikipage page ID	26666199 (xsd:integer)
page length (characters) of wiki page	3788 (xsd:nonNegativeInteger)
Wikipage revision ID	1039619536 (xsd:integer)
Link from a Wikipage to another Wikipage	Florida State University Logarithm of a matrix Projection (linear algebra) Algebra over a field American Mathematical Society Argument of a function Banach algebra Sequence Cauchy sequence Giovanni Battista Rizza Functions and mappings Hypercomplex numbers Mathematical analysis Quaternion Quaternionic analysis Series (mathematics) Hypercomplex number Split-complex number Square root of a matrix Clifford algebra Clifford analysis Complex analysis Eigendecomposition of a matrix Holomorphic functional calculus Motor variable Space (mathematics) Functional analysis Diagonalizable matrix Irene Sabadini Topology Mathematical Proceedings of the Cambridge Philosophical Society Physical mathematics Matrix (mathematics) Expm Polynomial Real analysis
has abstract	In mathematics, hypercomplex analysis is the extension of real analysis and complex analysis to the study of functions where the argument is a hypercomplex number. The first instance is functions of a quaternion variable, where the argument is a quaternion. A second instance involves functions of a motor variable where arguments are split-complex numbers. In mathematical physics, there are hypercomplex systems called Clifford algebras. The study of functions with arguments from a Clifford algebra is called Clifford analysis. A matrix may be considered a hypercomplex number. For example, the study of functions of 2×2 real matrices shows that the topology of the space of hypercomplex numbers determines the function theory. Functions such as square root of a matrix, matrix exponential, and logarithm of a matrix are basic examples of hypercomplex analysis. The function theory of diagonalizable matrices is particularly transparent since they have eigendecompositions. Suppose where the Ei are projections. Then for any polynomial The modern terminology for a "system of hypercomplex numbers" is an algebra over the real numbers, and the algebras used in applications are often Banach algebras since Cauchy sequences can be taken to be convergent. Then the function theory is enriched by sequences and series. In this context the extension of holomorphic functions of a complex variable is developed as the holomorphic functional calculus. Hypercomplex analysis on Banach algebras is called functional analysis. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Hypercomplex_analysis
is Link from a Wikipage to another Wikipage of	Giovanni Battista Rizza Glossary of areas of mathematics Hypercomplex number Motor variable Irene Sabadini Leave-one-out error Numerical analysis
is academic discipline of	Giovanni Battista Rizza
is known for of	Giovanni Battista Rizza
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Hypercomplex_analysis

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