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Complexification

In mathematics, the complexification of a vector space V over the field of real numbers (a "real vector space") yields a vector space VC over the complex number field, obtained by formally extending the scaling of vectors by real numbers to include their scaling ("multiplication") by complex numbers. Any basis for V (a space over the real numbers) may…

Products, Dickson doubling & Formal definition

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Overview

Formal definition

Basic properties

Examples

Dickson doubling

Complex conjugation

Linear transformations

Dual spaces and tensor products

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Map overview Semantic statistics

Complexification

Nodes55
Edges54
Triples47
Avg. degree1.96
Density0.036364
Components1

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Complexification

Top relations

related to References · 18
Complexification → Academic Press, Advanced Linear Algebra, Finite-Dimensional Vector Spaces, Graduate Texts, Group Representations, Halmos, Introduction, ISBN, Linear Algebra, Mathematics, New York, Paul, Roman, Ronald, Shaw, Springer, Steven, Vol
related to Dickson doubling · 12
Complexification → Cayley, Dickson, Doubling, Finally, If, It, Leonard Dickson, Next, One, The, Two, When
related to Formal definition · 6
Complexification → As, However, If, Let, More, The
related to Dual spaces and tensor products · 5
Complexification → Complex, Hom, HomR, That, The
related to Examples · 5
Complexification → Cn, Likewise, Rn, The, VC
is a · 1
Complexification → example of extension of scalars

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Important terminology

complex real displaystyle vector space vc linear mathbb given numbers conjugation tensor spaces isomorphism structure also product one map multiplication

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Complexificationis aexample of extension of scalars0.90text
Complexificationrelated to Dickson doublingThe0.60section
Complexificationrelated to Dickson doublingLeonard Dickson0.60section
Complexificationrelated to Dickson doublingOne0.60section
Complexificationrelated to Dickson doublingNext0.60section
Complexificationrelated to Dickson doublingTwo0.60section
Complexificationrelated to Dickson doublingFinally0.60section
Complexificationrelated to Dickson doublingWhen0.60section
Complexificationrelated to Dickson doublingIf0.60section
Complexificationrelated to Dickson doublingDoubling0.60section
Complexificationrelated to Dickson doublingCayley0.60section
Complexificationrelated to Dickson doublingIt0.60section

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