English Dictionary

complex line

名詞

迂言形

(complex analysis, analytic geometry) A 1-dimensional affine subspace of a vector space over the complex numbers.

日本語の意味

複素数体上のベクトル空間における1次元のアフィン部分空間。 / 数学（複素解析・解析幾何学）において、複素数で定義される線形空間の1次元アフィン部分空間。

The holomorphic map f: C -> C2 has its image contained in a complex line, so we can regard it as a holomorphic function to C.

正則写像 f: C -> C^2 の像が複素一次元アフィン部分空間に含まれているので、それを複素数値の正則関数として扱うことができます。

意味（1）

(complex analysis, analytic geometry) 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. The complex line in C ⁿ through a point A∈ C ⁿ in the direction of a vector B∈ C ⁿ is the one-dimensional complex submanifold of C ⁿ described parametrically as A+tB:t∈ C.

complex lines （ plural ）