Page 817 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

so an orthonormal basis for is

EXAMPLE 8 Orthonormal Set in Complex

Calculus Required

Let complex have the inner product of Example 3, and let W be the set of vectors in of the form

where m is an integer. The set W is orthogonal because if

are distinct vectors in W, then

If we normalize each vector in the orthogonal set W, we obtain an orthonormal set. But in Example 5 we showed that each
vector in W has norm , so the vectors

form an orthonormal set in complex .

Exercise Set 10.5

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Let and . Show that defines an inner product on .
1.

Compute using the inner product in Exercise 1.
2.