Purchase Solution

# Verifying an Inner Product for Continuous Functions

Not what you're looking for?

Please see the attached file for the fully formatted problems.

Suppose f(x) and g(x) are continuous real-valued functions defined for [0,1]. Define vectors in &#61690;n, F= ( f(x1), f(x2), ...,f(xn)) and G= g(x1), g(x2), ...,g(xn)), where xk = k/n. Why is <F,G>n = 1/n &#61669; f(xk) g(xk) dx not an inner product for the space of continuous functions?

##### Solution Summary

An inner product for continuous functions is verified. The solution is concise and well-presented.

##### Solution Preview

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

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.