線性獨立
Def：
If
is a nonempty set of a vector space , then the vector equation has at least one solution, the trivial solution. If this is the only solution, then is said to be linearly independent set, otherwise, is said to be a linearly dependent(線性相依) set.
向量與任何向量相依 S中部分向量相依則
線性相依，即線性獨立需要所有向量互相獨立。
Def2:
If
are functions that n-1 times differentiable on the interval , then the determinant is called the Wronskian of functions
Theorem(判斷一群函數是否線性獨立):
If the functions
have continuous derivatives on the interval and if the Wronskian of these functions is not identically zero on , then these functions form a linearly independent set of vectors in 在負無窮到正無窮區間n-1次可導的函數組，對於其Wronskian若存在
使得 則這群函數L.I.。若對所有的 都使得 則可能相依也可能獨立，屆時可以直接觀察函數之間的關係是否存在相依性。
Theorem(對於實數向量空間，向量集合內元素個數大於實數向量空間維度時一定相依):
Let
be a set of vectors in , if , then is L.D.