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Emeritus
PF Gold
P: 5,540
 Originally posted by lethe oh and i assume that you know what it means for vectors to be linearly independent,
Vectors vi (i=1,2,3,...) in Rn are independent iff

a1v1+a2v2+a3v3+...=0

implies that

a1+a2+a3+...=0

 and what a basis of a vector space is.
A set of vectors (v1,v2,v3,...) is a basis for a vector space V iff

1. v1,v2,v3,... span* V.
2. v1,v2,v3,... are independent.

*span(v1,v2,v3,...)={a1v1+a2v2+a3v3+...|for ai in R}

edit: fixed subscript bracket