219720 – Matrix Analysis

Semester: 1/2567
Classroom: SCB 4302, SCB 4305
Class meeting: M Th 9.30 am – 11.00 am
Instructor: Dr. Nattapol Ploymaklam
Office: MB 2225
Email: nattapol.p@cmu.ac.th

Documents

Midterm Exam Date: Sunday, August 25, 2024 at 12.00 – 15.00

Location: TBA

1. Matrix and Vector Space Review

1.1 Vector spaces

1.2 Inner product and norm

2. Eigenvalues, eigenvectors and similarity

2.1 Characteristic polynomial

2.2 Similarity

2.3 Left and right eigenvectors

3. Unitary, similarity and equivalence

3.1 Unitary matrices and QR factorization

3.2 Unitary similarity

3.3 Unitary and real orthogonal triangularization

3.4 Unitary equivalence and singular value decomposition

4. Canonical forms

4.1 The Jordan canonical form theorem

4.2 The real Jordan and Weyr canonical forms

4.3 Triangular factorization and canonical forms

Final Exam Date: Monday, October 28, 2024 at 8.00 – 11.00
Location: TBA

5. Hermitian matrices

5.1 Properties and characterizations of Hermitian matrices

5.2 Eigenvalue inequalities for Hermitian matrices

5.3 Unitary congruence and complex symmetric matrices

6. Locations and perturbation of eigenvalues

6.1 Geršgorin discs

6.2 Eigenvalue perturbation theorems

7. Positive definite and positive semidefinite matrices

7.1 Characterizations and properties

7.2 Polar and singular value decompositions

7.3 Schur product theorem

8. Positive and nonnegative matrices

8.1 Inequalities and generalities

8.2 Irreducible nonnegative matrices

8.3 General limit theorem