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Matrix Analysis, 6 credits
Matrisanalys, 6 hp
TATB10
Main field of study
Mathematics Applied MathematicsCourse level
Second cycleCourse type
Programme courseEducation components
Preliminary scheduled hours: 36 hRecommended self-study hours: 124 h
Available for exchange students
YesECV = Elective / Compulsory / Voluntary
The course syllabus is preliminary
Main field of study
Mathematics, Applied MathematicsCourse level
Second cycleAdvancement level
A1FCourse offered for
- Master of Science in Engineering Mathematics
- Master of Science in Applied Physics and Electrical Engineering - International
- Master of Science in Applied Physics and Electrical Engineering
- Master's Programme in Mathematics
Prerequisites
Linear Algebra, Honours Course or similar
Intended learning outcomes
After completing the course the student should be able to communicate, apply, model, analyze and solve problems by using the concepts and methods described in the course content.
Course content
Properties of matrix rank. Block matrices and Schur complement. Special matrices: Toeplitz, circulant, Vandermonde, Hankel, and Hessenberg matrices. Companion matrices. Real and complex canonical forms. Vector and matrix norms.
Eigenvalues: location, inequalities, perturbations, variational characterization.
Singular values: inequalities, variational characterization, low rank approximation for unitarily invariant norms.
Functions of matrices, power series. Matrix products: Kronecker, Hadamard and Khatri-Rao products. Linear and nonlinear matrix equations. Matrices of functions, matrix calculus and differentiation.
Multilinear algebra: rank, decomposition and approximation of tensors.
Teaching and working methods
Lectures and seminars with student presentations
Examination
| UPG1 | Assignments and projects | 6 credits | U, 3, 4, 5 |
UPG1 also includes oral and written presentations
Grades
Four-grade scale, LiU, U, 3, 4, 5Department
Matematiska institutionenCourse literature
Books
- Horn, Roger A., Johnson, Charles R., (2013) Matrix analysis. 2. ed. Cambridge ; New York : Cambridge University Press, 2013
ISBN: 9780521839402, 9780521548236
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| UPG1 | Assignments and projects | 6 credits | U, 3, 4, 5 |
UPG1 also includes oral and written presentations
Course literature is preliminary.
Books
Horn, Roger A., Johnson, Charles R., (2013) Matrix analysis. 2. ed. Cambridge ; New York : Cambridge University Press, 2013
ISBN: 9780521839402, 9780521548236
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (courses on G1X-level) |
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| 1.2 Fundamental engineering knowledge (courses on G1X-level) |
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| 1.3 Further knowledge, methods and tools in any of : mathematics, natural sciences, engineering (courses at G2X level) |
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Linear Algebra Intermediate Course/Upper Course |
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| 1.4 Advanced knowledge, methods and tools in any of: mathematics, natural sciences, engineering (courses at A1X level) |
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UPG1
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Matrix theory for modeling in technology and science, especially data analysis and AI |
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| 1.5 Insight into current research and development work |
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Insight into current research |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
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UPG1
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Application of theory to problem formulation, modeling and choice of solution methods. |
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| 2.2 Experimentation, investigation, and knowledge discovery |
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
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UPG1
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Creative and critical thinking, lifelong learning. |
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| 2.5 Ethics, equity, and other responsibilities |
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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| 3.2 Communications |
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UPG1
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Oral and written presentations of projects |
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| 3.3 Communication in foreign languages |
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Course language English |
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 Societal conditions, including economically, socially and ecologically sustainable development |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS | ||||||
| 5.1 Societal conditions, including economically, socially and ecologically sustainable development within research or development projects |
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| 5.2 Economic conditions for research or development projects |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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