Find the coordinate matrix of the function $\cos^2x$ relative to the ordered basis $\{1,\cos x,\sin x,\sin 2x\}$.
Find the coordinate matrix of the function $\cos^2x$ relative to the ordered basis $\{1,\cos x,\sin x,\sin 2x\}$.
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linear-algebra
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2This sounds like a command, not a question. You should give us some context for your problem, as well as what your ideas are so far. – 2012-12-15
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1Since when are sets ordered? – 2012-12-15
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0@akkkk: Sets are not generally ordered, but a basis is ordered so that the co-ordinates read off the basis becomes unique. – 2012-12-15
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1Since $\cos^2(x)$ is even and has period $\pi$ it is not an exact linear combination of the basis elements. If this is about approximation then this question needs more context. – 2012-12-15
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0I see that {1,sinx,cosx} generates cos^2 but how ı can find coordinate matrix? – 2012-12-15
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0@signum Then you see more than I do. – 2012-12-15
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0I don't think that given functions form a basis, since last element depends on third and second as $\sin 2x = 2 \sin x \cos x$ – 2012-12-15
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0@Kaster How's that a linear dependency? – 2012-12-15
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0@WimC I don't understand your question. – 2012-12-15
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0OK, gotcha, those are linearly independent. My bad. – 2012-12-15
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0Should that $\sin 2x$ maybe be $\sin^2 x$? – 2012-12-15