术语“线性变换”的详细信息

英译术语:

linear transformation

汉语语境:

在数学中，线性映射（也叫做线性变换或线性算子）是在两个向量空间之间的函数，它保持向量加法和标量乘法的运算。术语“线性变换”特别常用，尤其是对从向量空间到自身的线性映射(自同态)。在抽象代数中，线性映射是向量空间的同态，或在给定的域上的向量空间所构成的范畴中的态射。

英语语境:

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping V → W between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication. Linear maps can generally be represented as matrices, and simple examples include rotation and reflection linear transformations.