219720 – Matrix Analysis

Semester: 1/2568
Classroom: SCB 4302, SCB 4305
Class meeting: T F 11.00 am – 12.30 pm
Instructor: Nattapol Ploymaklam
Office: MB 2225
Email: nattapol.p@cmu.ac.th

Documents

Midterm Exam Date: Wednesday, August 27, 2025 at 15.30 – 18.30

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

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

Final Exam Date: Friday, October 24, 2025 at 12.00 – 15.00
Location: TBA

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