Explore BrainMass

# Vector Spaces of Complex Valued Polynomials, Complex Inner Products and Orthonormal Sets

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Let V be the vector space of all complex valued polynomials defined over the half line [0,infinity).

(a) Show that <f,g> = &#8747; 0-->&#8734; f(x) ( g(x) bar) e^-x dx is a complex inner product on V
g(x) bar is g(x) with a bar on it, which I believe to be the conjugate.

(b) Find an orthonormal set : {f_o, f_1} in V such that span{e_o,e_1} = span{f_o,f_1}, where e_o(x) = 1 and e_i(x) = x.

Â© BrainMass Inc. brainmass.com November 24, 2021, 12:01 pm ad1c9bdddf
https://brainmass.com/math/vector-calculus/complex-inner-products-orthonormal-sets-64778

#### Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Let be the vector space of all complex valued polynomials defined over ...

#### Solution Summary

Vector Spaces of Complex Valued Polynomials, Complex Inner Products and Orthonormal Sets are investigated. The solution is detailed and well presented.

\$2.49