Several complex variables | Topological vector spaces

Complex coordinate space

In mathematics, the n-dimensional complex coordinate space (or complex n-space) is the set of all ordered n-tuples of complex numbers. It is denoted , and is the n-fold Cartesian product of the complex plane with itself. Symbolically, orThe variables are the (complex) coordinates on the complex n-space. Complex coordinate space is a vector space over the complex numbers, with componentwise addition and scalar multiplication. The real and imaginary parts of the coordinates set up a bijection of with the 2n-dimensional real coordinate space, . With the standard Euclidean topology, is a topological vector space over the complex numbers. A function on an open subset of complex n-space is holomorphic if it is holomorphic in each complex coordinate separately. Several complex variables is the study of such holomorphic functions in n variables. More generally, the complex n-space is the target space for holomorphic coordinate systems on complex manifolds. (Wikipedia).

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Complex Numbers as Vectors (2 of 3: Subtraction)

More resources available at www.misterwootube.com

From playlist Complex Numbers

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This video introduces cylindrical coordinates and shows how to convert between cylindrical coordinates and rectangular coordinates. http://mathispower4u.yolasite.com/

From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates

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Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Space Coordinates Plotting Points in 3 Dimensions

From playlist Calculus 3

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From playlist Special Relativity

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The Equations of the Coordinate Planes in R3

This video identifies the three coordinate planes in the 3D coordinate system. Site: http://mathispower4u.com

From playlist Equations of Planes and Lines in Space

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From playlist Physics

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Ex: Identifying the Coordinates of Points on the Coordinate Plane

This video explains how to determine the coordinates of points on the coordinate plane. Complete Video List at http://www.mathispower4u.com Search by Topic at http://www.mathispower4u.wordpress.com

From playlist The Coordinate Plane, Plotting Points, and Solutions to Linear Equations in Two Variables

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More resources available at www.misterwootube.com

From playlist Complex Numbers

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From playlist Mathematics

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From playlist Cauchy-Riemann Equations in Higher Dimensions 2019

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Simon Donaldson - Introduction to Differential geometry on toric varieties [2013]

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From playlist Mathematics

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B. Deroin - Monodromy of algebraic families of curves (Part 2)

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From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications

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Colloquium MathAlp 2019 - Claude Lebrun

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From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

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From playlist The Riemann Sphere

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Tom Sutherland: Stability conditions and flat connections

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From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"

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Field Equations 2 - The Klein-Gordon Equation

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From playlist QED- Prerequisite Topics

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Jie Liang: Non-Diffusive Vortexes at Transition State of Activated Process by Persistent Homology

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From playlist AATRN/STMS

Related pages

Bijection | Complex plane | Tuple | Complex number | Dimension | Euclidean topology | Mathematics | Holomorphic function | Vector space | Real coordinate space | Cartesian product | Topological vector space | Complex manifold