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Originally posted by lethe
oh and i assume that you know what it means for vectors to be linearly independent,
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Vectors vi (i=1,2,3,...) in R n are independent iff
a 1v1+a 2v2+a 3v3+...=0
implies that
a 1+a 2+a 3+...=0
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and what a basis of a vector space is.
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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,...)={a 1v1+a 2v2+a 3v3+...|for a i in R}
edit: fixed subscript bracket
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