MTH 525, FALL 2006

Brief Notes for Weeks 12 & 13

(tentative)

Monday, November 13

Assignment 10 is collected.

We introduce inner products in preparation for the study of inner product spaces, Chapter 8.

We define inner product and give some examples. We define quadratic form.

Do p. 275.

We define innter product spaces and basic properties (Theorem 1) of an inner product on an inner product space. We define orthogonal and orthonormal. Theorems 2 (a set of orthogonal vectors is independent) and 3 motivate the study, since they show that inner products give us “good” sets of bases. We study orthogonal projections (Theorem 4.)

Wednesday, November 15

We study linear functionals and adjoints (section 8.3) and unitary operators (section 8.4)

Monday, November 20

We study unitary and normal operators (sections 8.4 and 8.5.)

Last modified October 1, 2006