# linear independence

Definition from Wiktionary, the free dictionary

## English[edit]

### Noun[edit]

**linear independence** (*uncountable*)

- (algebra) the state of being linearly independent
*The***linear independence**of a set of vectors can be determined by calculating the Gram determinant of those vectors; if their Gram determinant is zero, then they are linearly dependent, and if their Gram determinant is non-zero, then they are linearly independent. Incidentally, the same Gram determinant can be used to calculate the hyper-volume of a hyper-parallelepiped (whose edges which "radiate" from an "origin" vertex are described by the vectors).