Complex line

In mathematics, a complex line is a one-dimensional affine subspace of a vector space over the complex numbers. A common point of confusion is that while a complex line has dimension one over C (hence the term "line"), it has dimension two over the real numbers R, and is topologically equivalent to a real plane, not a real line.

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Geometry Complex analysis Geometry stubs Wikimedia Foundation. 2010. Игры ⚽ Нужен реферат? The Water Goblin Johanna Goldsmith Look at other dictionaries: Complex projective space — The Riemann sphere, the one dimensional complex projective space, i.e. the complex projective line. In mathematics, complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a …   Wikipedia Complex plane — Geometric representation of z and its conjugate in the complex plane. The distance along the light blue line from the origin to the point z is the modulus or absolute value of z. The angle φ is the argument of z. In mathematics …   Wikipedia Line integral — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiation Taylor s theorem Related rates …   Wikipedia Line bundle — In mathematics, a line bundle expresses the concept of a line that varies from point to point of a space. For example a curve in the plane having a tangent line at each point determines a varying line: the tangent bundle is a way of organising… …   Wikipedia Complex polytope — A complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one. On a real line, two points bound a segment. This defines an… …   Wikipedia Line at infinity — Ideal line redirects here. For the ideal line in racing, see Racing line. In geometry and topology, the line at infinity is a line which is added to the real (affine) plane in order to give closure to, and remove the exceptional cases from, the… …   Wikipedia Complex cobordism — In mathematics, complex cobordism is a generalized cohomology theory related to cobordism of manifolds. Its spectrum is denoted by MU. It is an exceptionally powerful cohomology theory, but can be quite hard to compute, so often instead of using… …   Wikipedia Complex space — In mathematics, n dimensional complex space is a multi dimensional generalisation of the complex numbers, which have both real and imaginary parts or dimensions. The n dimensional complex space can be seen as n cartesian products of the complex… …   Wikipedia Complex — A complex is a whole that comprehends a number of intricate parts, especially one with interconnected or mutually related parts; for example, a complex of buildings. Complex may refer to: Contents 1 Biology 2 Chemistry …   Wikipedia Complex convexity — Definition A set Ω in is called convex if its intersection with any complex line is contractible. Background In complex geometry and analysis, the notion of convexity and its generalizations play an important role in understanding function… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”