Linear Algebra and Its Applications · Problem 3.4.20

Orthogonality — Gilbert Strang

Mathematics · hilbert-space-inner-products

Problem

In Hilbert space, find the length of the vector

v = (1/\sqrt{2}, 1/\sqrt{4}, 1/\sqrt{8}, \ldots)

and the length of the function

f(x) = e^x

(over the interval

0 \leq x \leq 1

). What is the inner product over this interval of

e^x

and

e^{-x}