1. The set of vectors {u, v, w} is orthonormal because each vector has a length of 1 and they are mutually perpendicular.
这组向量{u，v，w}是正交归一的，因为每个向量的长度为1，且彼此垂直。

2. To find the orthonormal basis for the subspace, we need to orthogonalize the basis vectors and then normalize them.
要找到子空间的正交归一基，我们需要将基向量正交化，然后归一化。

3. The Gram-Schmidt process is a common method for transforming a set of vectors into an orthonormal basis.
格拉姆-施密特过程是将一组向量转换为正交归一基的常用方法。

4. The orthonormality of the basis vectors ensures that any vector in the space can be uniquely represented as a linear combination of the basis vectors.
基向量的正交性确保空间中的任何向量都可以被唯一地表示为基向量的线性组合。

5. The Fourier basis is an example of an orthonormal basis in the space of periodic functions.
傅里叶基是周期函数空间中的一个正交归一基的例子。

6. The orthonormality condition allows us to easily compute the inner product of two vectors in a vector space.
正交归一条件使我们能够轻松计算向量空间中两个向量的内积。