# linear independence

linear independencenoun

The property of a set of vectors of having no linear combinations equal to zero unless all of the coefficients are equal to zero.

## linear-independence

Noun

(*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).*