摘要: 数学中的变换种类多样，作用广泛。本文从几何和代数两个方面对数学中几种常见的变换做了简单的研究，并对其在数学中的应用做了举例和说明。线性变换是线性空间中的重要变换，正交变换是其中一种重要的变换。参量变换和恒等变换是通过形式（变量）的转换简化所求问题。仿射变换是几何中的一个重要变换，它是从运动变换到射影变换的桥梁。轴对称变换、平移变换、旋转变换、相似变换是初等几何中几种重要的图形变换，通过图形变换的性质可以更好解决问题。

关键词:线性变换; 参量变换; 恒等变换； 几何变换

Abstract: There are many mathematical transformations in mathematics. In this paper, it   summarizes the definition of transformations. It also summarizes it’s application of problem-solving in mathematics. Linear transformation with it’s special form identically equal transformation play an important effect in linear space. Parameter transformation and  identically equal through a variable or form to simplify questions. Affine transformation plays an important role in geometry, it is the transition from the movement to transform projective transform. Axis of symmetry transformation、translation transformation 、 rotation transformation and similarity transformation are several important graph transformation in elementary geometry, through graphics transform nature can better solve the problem.

Keywords: Linear transformation ； Identically equal transformation;　Parameter transformation；Geometry transformation