线性映射
Also known as linear mapping, linear transformation, linear function, linear homomorphism, linear mapped
保留加法和標量乘法運算的映射
AI overview
A linear map is a type of mathematical function that preserves two basic operations: when you add inputs together, the output is the same as adding the outputs separately, and when you multiply an input by a number, the output gets multiplied by that same number. Linear maps matter because they're fundamental tools in mathematics and science for describing relationships between quantities that scale and combine in predictable, proportional ways.
AI-generated from the Wikipedia summary — may contain errors.
Article · 中文
在数学中，线性映射（有的书上将“线性变换”作为其同义词，有的则不然）是在两个向量空间（包括由函数构成的抽象的向量空间）之间的一种保持向量加法和标量乘法的特殊映射。线性映射从抽象代数角度看是向量空间的同态，从范畴论角度看是在给定的域上的向量空间所构成的范畴中的态射。 “线性算子”也是与“线性映射”有关的概念。但是不同数学书籍上对“线性算子”的定义存在区别。在泛函分析中，“线性算子”一般被当做“线性映射”的同义词。而有的书则将“线性算子”定义为“线性映射”的自同态子类（详见下文）。为叙述方便，本条目在提及“线性算子”时，采用后一种定义，即将线性算子与线性映射区别开来。
Abstract from DBpedia / Wikipedia · CC BY-SA