Orthogonal transformation is a common concept in higher algebra and linear algebra. At present, there are two ways to define this concept in different textbooks. The linear transformation σ that defines Euclidean space v as 1 is called orthogonal transformation. If it keeps the length of the vector constant, that is, for any α∈V, there is σ (α) = | α |. The linear transformation σ that defines 2 Euclidean space V is called orthogonal transformation. If it keeps the inner product of the vector unchanged, there is an orthogonal transformation with = for any α β∈ V. The closest concept is linear transformation, and keeping the length of the vector unchanged and the inner product of the vector unchanged are two characteristics of orthogonal transformation respectively. On the premise that σ is a linear transformation, it can be proved that these two types of features are equivalent, so the definition of 1 is consistent with the concept described in definition 2.