Advanced Linear Algebra
《Advanced Linear Algebra》 · 第 47 页 · Chapter 1「The Dimension of a Vector Space」（Theorem 1.9 之后）
The following are equivalent: $S$ is linearly independent and spans $V$; every nonzero vector in $V$ is an essentially unique linear combination of vectors from $S$. A set of vectors in $V$ that satisfies either condition is called a basis for $V$.