From what I understand, a basis is essentially a subset of a vector space over a given field.(adsbygoogle = window.adsbygoogle || []).push({});

Now what I'm not so sure of is the linearly independence part. If the basis has two linearly independent vectors, then than means they aren't collinear: rather, they wouldn't have the same slope or be generated by each other?

let's say a vector v[itex]\epsilon[/itex]V is (v[itex]_{1}[/itex], v[itex]_{2}[/itex],...,v[itex]_{n}[/itex])

and a vector w[itex]\epsilon[/itex]V is (w[itex]_{1}[/itex], w[itex]_{2}[/itex],...,w[itex]_{n}[/itex])

such that

v [itex]\neq[/itex] cw.

for any constant c[itex]\epsilon[/itex][itex]\textbf{F}[/itex]

These would then be non-collinear which means there are no linear operators that can turn v into w?

Any insight would be greatly appreciated and thank you in advance.

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# Interpretation of a Basis

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