Read Sections 1-4 and Section 8 of Chapter 7 of the text, about inner products and unitary diagonalization.
The following problems give you practice with the concepts in Chapter 7. Some are very easy, some hard; some may be done in class. You might first browse through the problems and see which you can do easily and which are more demanding. Be sure to try the quizzes at the end of each chapter. They're quick True/False and multiple choice questions, and they have answers in the back of the book.
No homework will be collected from this chapter, but some of the material will turn up on the final exam.
Chapter 7
Section 1, p. 307 #1b,2,3a,5
Section 2, p. 315 #2,6,7,11
Section 3, p. 324 #1,3,5a,6,8
Section 4, p. 334 #1,3,4,5,9bdg,11
End of Chapter quiz, p. 359 Try this; all questions have answers in the back.