binbagsss
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The question is : If the vector space C[1,1] of continuous real valued functions on the interval [1,1] is equipped with the inner product defined by (f,g)=[itex]^{1}_{-1}[/itex] [itex]\intf(x)g(x)dx[/itex]
Find the linear polynomial g(t) nearest to f(t) = e^t?
So I understand the solution will be given by (u1,e^t).||u1|| + (u2,e^t).||u2||
But I am having trouble understanding what u1 and u2 should be. I understand they must be othorgonal and basis for a subspace S [itex]\in[/itex] C[-1,1].
However I am not too sure what dimension this basis should be of, and not 100% sure what is meant by the vector space C[-1,1].
(The solution uses 1 and t as u1 and u2...)
Many thanks in advance for any assistance.
Find the linear polynomial g(t) nearest to f(t) = e^t?
So I understand the solution will be given by (u1,e^t).||u1|| + (u2,e^t).||u2||
But I am having trouble understanding what u1 and u2 should be. I understand they must be othorgonal and basis for a subspace S [itex]\in[/itex] C[-1,1].
However I am not too sure what dimension this basis should be of, and not 100% sure what is meant by the vector space C[-1,1].
(The solution uses 1 and t as u1 and u2...)
Many thanks in advance for any assistance.
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