complex line
complex line noun: a 1-dimensional affine subspace of a vector space over the complex numbers.
Noun
complex line (plural complex lines)
- A 1-dimensional affine subspace of a vector space over the complex numbers.
- However, it is possible to characterize the real parts of holomorphic functions of several variables at least locally as those continuous functions such that their restrictions to all complex lines, not just to complex lines parallel to the coordinate axes, are real parts of holomorphic functions....1990, R. C. Gunning, Introduction to Holomorphic Functions of Several Variables, Volume 1 Function Theory, Wadsworth & Brooks/Cole, page 102
- A complex line in #92;Cⁿ is a set of the form l#61;#92;#123;z#58;z#61;a#43;#92;lambdab,#92;lambda#92;in#92;C#92;#125;, where a and b are fixed points in #92;Cⁿ, with b#92;ne 0. Let us say that l is the complex line through a in the “direction” b.2014, Paul M. Gauthier, Lectures on Several Complex Variables, Springer (Birkhäuser), page 39
- Synonyms:
- complex plane
Synonyms of complex line
Forms of complex line
| plural | complex lines |
|---|
Words formed from complex line
- complex line bundle
Questions about complex line
- What does complex line mean?
- Complex line means a 1-dimensional affine subspace of a vector space over the complex numbers.
- What part of speech is complex line?
- Complex line is a noun.
- What is the plural of complex line?
- The plural of complex line is complex lines.
Words near complex line in the dictionary
Source and license
Adapted from Wiktionary: complex line (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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