Reading Assignment:

• Read Section 4.1 for Wednesday Nov. 20
• Read Section 4.2 for Friday Nov 22
• Read Section 4.3 for Monday Nov 25
• Read Section 4.4 for Monday Nov 25

Homework Assignment:

• Due Nov 25
  • Sec. 3.8: 3, 7, 11
  • Sec. 3.9: 1, 12
  • Sec. 4.1: 3, 4, 13, 19
  • Sec. 4.2: 9, 14, 15, 17, 25, 26, 27, 28
• Due Dec 4
  • Sec. 4.3: 3, 4, 14-17, 19, 25
  • Sec. 4.4: 1, 3, 8, 9, 11, 14, 30
  • Sec. 4.5: 4, 5, 6, 12, 14, 18, 21, 22, 28

• linear tranformation
• the identity, dialations, and contractions
• the matrix of a linear tranformation
• the null space and range of a linear transformation
• rank and nullity
• the rank plus nullity theorem
• orthogonal linear transformations
• rotations and reflections

• The least-squares optimization problem
• the least-squares residual vector
• the least-squares solution
• consistency of the least-squares problem
• the normal equations
• the gradient of the least-squares objective
• full rank
• rank deficient matrices
• existence and uniqueness criteria for least-squares problems

• Eigenvalues and eigenvectors
• Eigenvalues and eigenvectors for 2 by 2 matrices
• the relationship between eigenvalues and the singularity of A-aI
• determinants and eigenvalues
• the determinant of an n by n matrix
• Laplace's formulas for the determinant