Noun
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).
Matrix methods are significantly limited for MIMO systems where linear independence cannot be assured in the relationship between inputs and outputs. Source: Internet
Allowing more linear combinations in this case can also lead to a different concept of span, linear independence, and basis. Source: Internet
Then: : and and Subtracting the first equation from the second, we obtain: : so Adding this equation to the first equation then: : Hence we have linear independence. Source: Internet