Is the set linearly independent?

#I have a vague kind of idea that those functions form a linearly independent set but only on [0,2pi]. Could anyone give me some advice on this? Thanks very much

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- Oct 13th 2010, 04:51 PMslevviolinearly independent
Is the set linearly independent?

#I have a vague kind of idea that those functions form a linearly independent set but only on [0,2pi]. Could anyone give me some advice on this? Thanks very much - Oct 14th 2010, 05:02 AMHallsofIvy
Yes, they form a linearly independent set on the entire real line, not just . Indeed,

**because**they are periodic with period , whatever is true of them on is true for all x. - Oct 14th 2010, 08:09 AMslevvio
Thanks! is there a way to prove that those functions are linearly independent in a simple way? It's easy to show if i take 2 functions out of it

ie but I am having trouble doing it for an arbitrary subset