linear independence

Noun

Meaning

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).

Source: en.wiktionary.org

Synonyms

linear operator

Examples

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

Close letter words and terms

linear homomorphism linear homotopy linear hydrocarbon chain linear lambda calculus linear leaf linear learning