## Quick Reference

A fundamental concept in mathematics. Let

*x*_{1}, *x*_{2},…, *x*_{n}

be *m*-component vectors. These vectors are linearly independent if for some scalars

α_{1}, α_{2},…, α_{n}

, implies

α_{1} = α_{2} = … = α* _{n}* = 0

Otherwise the vectors are said to be linearly dependent, i.e. at least one of the vectors can be written as a linear combination of the others. The importance of a linearly independent set of vectors is that, providing there are enough of them, any arbitrary vector can be represented uniquely in terms of them.

A similar concept applies to functions

*f*_{1}(*x*), *f*_{2}(*x*),…, *f** _{n}*(

*x*)

defined on an interval [*a*,*b*], which are linearly independent if for some scalars

α_{1}, α_{2},…, α_{n}

, the condition, for all *x* in [*a*,*b*], implies

α_{1} = α_{2} = …= α* _{n}* = 0

*Subjects:*
Computing.

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