Linear Algebra and Its Applications · Problem 3.4.22

Orthogonality — Gilbert Strang

Mathematics · fourier-coefficient-minimization

Problem

By setting the derivative to zero, find the value of b1b_1 that minimizes ∥b1sin⁡x−cos⁡x∥2=∫02π(b1sin⁡x−cos⁡x)2dx.\|b_1 \sin x - \cos x\|^2 = \int_0^{2\pi} (b_1 \sin x - \cos x)^2 dx. Compare with the Fourier coefficient b1b_1.

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