Vectors/Linearly independent/Explanations/Remark

If a family is not linearly independent, then it is called linearly dependent. A linear combination ${}\sum _{i\in I}s_{i}v_{i}=0$ is called a representation of the null vector. It is called the trivial representation if all coefficients ${}s_{i}$ equal ${}0$ and, if at least one coefficient is not ${}0$, a nontrivial representation of the null vector. A family of vectors is linearly independent if and only if one can represent with the family the null vector only in the trivial way. This is equivalent with the property that no vector of the family can be expressed as a linear combination by the others.