We have seen that the space C-1, 1] with (S. 9) = | s (x) g (x2) dar is an inner product space. Let U = {f € C[-1,1] : f(-x) = f (x)}, W = {f€C[-1, 1] f(-x) = -f (x)}. I.e., U and W are the set of even and odd functions in C[-1, 1], respectively. (a) Find an example of an even function and an example of an odd function.

We have seen that the space C-1, 1] with (S. 9) = | s (x) g (x2) dar is an inner product space. Let U = {f € C[-1,1] : f(-x) = f (x)}, W = {f€C[-1, 1] f(-x) = -f (x)}. I.e., U and W are the set of even and odd functions in C[-1, 1], respectively. (a) Find an example of an even function and an example of an odd function.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 15EQ

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