Matrix Calculus

Lecturer:

Miroslav Dont

Tutor:

Miroslav Dont

Supervisor:

Department of Mathematics

Synopsis:

Similar matrices. Jordan blocks, Jordan canonical matrices. Real canonical form of a real matrix. Characteristic and minimal polynomial. Caley-Hamilton thoerem. Functions of matrices, exponential matrix. Symetric, orthogonal and positive matrices. Diagonalization of symetric, positive and circulant matrices. Singular value decomposition. Moore-Penrose pseudoinverse matrix. Generalized solution of systems of linear equations.

Requirements:

Syllabus of lectures:

Syllabus of tutorials:

Study Objective:

Study materials:

1. F. Zhang: Matrix Theory, Basic Results and Techniques. Springer, 1999

2. D. S. Bernstein: Matrix Mathematics: Facts, and Formulas with Application to Linear Systems. Princeton Univ. Press, 2005

Note:

Time-table for winter semester 2011/2012:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue	roomT2:E1-103a Dont M. 11:00–12:30 (lecture parallel1) Dejvice haly CvičebnaroomZ4:B2-326 Dont M. 12:45–13:30 (parallel nr.101) Zikova ulice Konzultační místnost
Fri
Thu
Fri

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans:

• Doctoral studies, daily studies (compulsory elective course)
• Doctoral studies, combined studies (compulsory elective course)
• Doctoral studies, structured daily studies (compulsory elective course)
• Doctoral studies, structured combined studies (compulsory elective course)