Complex number space
I call the meeting that the whole prioritized n-tuple consisting of the complex number makes the double bare n-dimension (number) space (すうくうかん British: complex n-space) in the mathematics and write it with Cn. If it is n-重 Tsumoru Descartes of meeting C which the whole complex number makes and writes this in a sign
である. Each variable zi of the number of double bare n-dimensions space is called a coordinate or a coordinate ingredient (double bare). I call it the n-dimension double bare coordinates space (n-dimensional complex coordinate space) in a meaning called the space that the whole n-dimension double bare coordinates makes.
Table of contents
Structure on the number space
In the number of double bare space, the sum and the scalar every ingredient become the vector space in the complex number health by doubling it (they can make bijection between double bare n-dimension space Cn and true 2n-dimension space R2n if they think about the real part of each coordinate ingredient and an imaginary part). Furthermore, I put normal phase (standard Euclid phase ), and Cn makes phase linear space in the complex number health.
Function on the number space
When a function defined on an open set of the double bare n-dimension space is Masanori, I say when it becomes the Masanori function about each coordinate variable each. The many variables double bare functions theory is a study of the Masanori function of the n-variable. Generally the double bare n-dimension coordinate space is 接空間 for the Masanori coordinate system in double bare manifolds.
Allied item
- Coordinate space ( )
References
- Gunning, Robert; Rossi, Hugo, Analytic functions of several complex variables
This article is taken from the Japanese Wikipedia Complex number space
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