how to solve question d) ? For function space C [- pi, pi ] an inner product is

Question

how to solve question d) ?

For function space C [- pi, pi ] an inner product is defined as: Find the norm of sinx(x). Find the norm of sinx(2x). Show that sin(x) is orthogonal to sin(2x). d) Consider the set of {sin(x), sin(2x)} as an orthogonal basis for a subspace of C [- pi , pi ]. Find the orthogonal projection of f (x) = x into the subspace that is spanned by the given basis. (This orthogonal projection is the best approximation of f(x) = x using sin(x) and sin(2x) in the interval [ - pi , pi ])

Explanation / Answer

here orthogal projection of f(x) on sinx will be sinx on the interval (- )

and f(x) on sin2x will be   xsin2x on the interval (- )

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.