Please ignore all "least squares" and "complex numbers" problems (Sections 5.5 and 6.5 in the text). But I will ask you about the Gram-Schmidt process (Section 6.4).
Complex numbers will not be on this exam, nor on the final. The least squares methods will be on the final exam.
List of definitions which may appear on the midterm:
Do not memorize definitions without understanding them!
Definition of coordinates, p.234
Definition of dimension, p.245
Definition of rank, p.253
Definition of change-of-coordinate matrix, p.261
Definition of eigenvalues and eigenvectors, p.271
Definition of the characteristic equation, p.281
Definition of similarity (p. 282) and of diagonalizability (p. 288)
Defintion of a matrix relative to coordinates, p.296
Definitions of length, distance, orthogonality, Section 6.1
Definition of orthogonal projection, p.326
List of proofs which may appear on the midterm:
Chapter 4, Theorem 7 (proof on p.234)
Chapter 4, Theorem 8 (proof on p.238)
Chapter 4, Theorems 9,10 (proofs on pp.244,245)
Chapter 4, Theorem 14 (proof on 253 or a different presentation in lecture)
Chapter 5, Theorem 2 (proof on p.275)
Chapter 5, Theorem 4 (proof on p.283 or a different presentation in lecture)
Chapter 5, Theorem 5 (proof on p.289)