The future tests, midterm 2 and the final, will be based on the topics covered in the lectures, and the problems assigned weekly.

• Notes: On matrix (revised), On Jordan form, On Polar Form
• Notes: lecture13-14, lecture 15, Lecture 16, Lecture 17, 5/11, 5/14, 5/16, 5/18, 5/21, 5/23, 5/25, 5/30, 6/1.

Syllabus

Week I

• (4/2) Vector spaces, subspaces, linear combinations, direct sums (Chapter 1)
• (4/6): definition of vector spaces, subspaces (Chapter 1)
• (4/8): sums and direct sums.(Chapter 1)

Week II (Apr. 9)

• Linear independence, basis, dimension (Chapter 2)

Week III (Apr. 16)

• Linear maps (Chapter 3)

Week IV (Apr. 23)

• Isomorphisms (Chapter 3)
• complex polynomials (Chapter 4)
• Eigenvalues and Eigenvectors (Chapter 5)

Week V (Apr. 30, lecture13-15)

• Eigenvalues and eigenvectors (Chapter 5)
• Generalized eigenvectors, Jordan normal form (approach different from Chapter 8)

Week VI (May 7)

• Jordan normal form (approach different from Chapter 8)
• Characteristic polynomial,minimal polynomial (approach different from Chapter 8)
• Trace and determinant (approach different from Chapter 10)
  

Week VII (May 14)

• Determinant, characteristic polynomial (approach different from Chapter 10)
• minimal polynomial, operators on real vector spaces (approach different from Chapter 9)
• Inner products, orthonormal bases (Chapter 6)

Week VIII (May 21)

• Inner products, orthonormal bases, linear functionals, adjoints (Chapter 6)
• Friday: midterm 2, from 9:00-10:30.

Week IX (May 28)

• May 29 (holiday)
• Self-adjoint and normal operators, Spectral Theorem (Chapter 7)

Week X (June 4)

• Review
• June 6 (last lecture) problem solving

Week XI

• June 12: test III 9:00-11:00.

 

 

Preparing Midterm One.