Linear Operators, Inner Products and Adjoints
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We are studying an inner product spaces. See attached file for full problem description.
Let V be a C-space of all complex valued polynomials with an inner product....
(i) Let p be a polynomial and let Mp: V-> V be a linear operator that is given by
Mp (q) :=p⋅q. Show that operator Mp has an adjoint and find it.
(ii) Let D: V-> V be a linear operator that maps every polynomial in its derivative , by
other words D(p) = p′ . Show that D has not an adjoint.
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Linear Operators, Inner Products and Adjoints are investigated. The response received a rating of "5/5" from the student who originally posted the question.
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The definition of operator M^* adjoint to operator M is that <M^*q|r> = <q|Mr> for all q and r in V.
(i) If M_p r = pr, than
<q | M_p r> = int q(t) bar [ p(t) r(t) ] dt = ...
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