CoursePlan_161317_39971.docx

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Zarqa University Instructor:

Faculty of Science Lecture’s time:

Department: Mathematics Semester:

Course title: Matrix Theory Office Hours:

Course description:

This course briefly reviews some basic concepts and results in linear algebra course and concerns with several topics on matrices, including: special types of matrices, eigenvalues and eigenvectors, normal forms, singular value decomposition, norms and some related subjects.

Aims of the course:

Upon completion of this course, the student should be able to

1. Determine the characteristic polynomial and minimal polynomial of square matrices.

2. Write Jordan canonical form of square matrices.

3. Recognize new types of matrices (Hermetian, Normal, Unitary and Positive definite).

4. Recognize normal form.

5. Find singular values of matrices.

6. Recognize singular value decompositions of matrices.

7. Find the generalized inverse of matrices.

8. Find some matrix norms for square matrices.

9. Find the maximum and minimum of quadratic forms.

10. Determine the least squares solution of linear systems.

11. Apply the LU factorization to solve systems of linear equations.

Intended Learning Outcomes: (ILOs)

A.

Knowledge and Understanding A1. Concepts and Theories:

1. Illustrate the concept of vector spaces, span , linear independence, basis and dimension.

2. Define and illustrate the concept of characteristic polynomial and minimal polynomial.

3. Define and illustrate the concept of Geometric and algebraic multiplicity.

4. Recognize new types of matrices (Hermetian, Normal, Unitary and Positive definite).

5. Define and illustrate the concept of similarity and unitary equivalence.

6. Define and illustrate the concept of singular values and condition numbers.

7. Define and illustrate the concept of matrix norms.

A2. Contemporary Trends, Problems and Research:

1. Comprehend Spectral theorem.

2. Comprehend Cayley-Hamilton theorem.

3. Comprehend the meaning of Jordan canonical form, normal form, singular value decompositions and the generalized inverse.

4. Comprehend Schur's Theorem.

5. Comprehend the meaning of the least squares solution.

A3. Professional Responsibility:

1. Reach to new properties of matrices via given theorems and results.

B.

Subject-specific skills B1. Problem solving skills:

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1. Solve systems of linear equations by different methods.

2. Find the generalized inverse of matrices.

3. Find the maximum and minimum of quadratic forms.

4. Find the least squares solution of linear systems.

B2. Modeling and Design:

Write the corresponding coefficients matrix of a system and apply on it elementary row operations to attain the solutions

B3. Application of Methods and Tools:

1. Use LU factorization to solve systems of linear equations.

2. Use matrix properties to find the maximum and minimum of quadratic forms

C.

Critical-Thinking Skills C1.Analytic skills:

Critically analyze and construct mathematical arguments related to matrices C2.Strategic Thinking:

Reach to new results by combining different theorems.

C3. Creative thinking and innovation:

Construct a proof of theorems.

D.

General and Transferable Skills (other skills relevant to employability and personal development) D1. Communication:

Effectively communicate in the field of mathematics by conducting discussions and participating in class, asking questions intended to encourage the exchange of ideas in class.

D2.Teamwork and Leadership:

Fostering an ability to work together in teams, engaging in group work, and to develop skills motivating others to accomplish goals.

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Course structures:

Week Credit

Hours ILOs Topics Teaching

Procedure Assessment methods

1 3 A1, B1, B2,

D1 Systems of linear equations, Gaussian elimination, Inverse, Determinant.

Lectures, cooperative learning and discussion

Homework's , Quiz and Exams

2 3 ^{A1, D1} Vector spaces, Span, Linear

independence, Basis and dimension.

Lectures, cooperative

learning and discussion Homework's , Quiz and Exams

3 3 ^{A1, A2, D1} Eigenvalues and eigen vectors,

Characteristic equation and characteristic polynomial, Spectral theorem.

4 3 A1, A2, A3,

C1, D1 Geometric and algebraic multiplicity, Minimal

polynomial, Cayley-Hamilton theorem.

5 3 A1, A3, C1,

C2,C3, D1 Similarity, Diagonalization, Lectures, cooperative

6 3 A1, A2, D1,

D2 Jordan canonical form Lectures, cooperative

First Exam

7 3 ^{A1, C1, D1} Hermitian matrices, Euclidean

inner product.

8 3 A1, A2, C1,

C2, C3, D1, Unitary matrices, Unitary equivalence, Schur’s theorem.

9 3 A1, A2, C1,

C2, D1 Normal matrices, Positive matrices.

10 3 A1, A2, C1,

C2 Singular values, Singular value decomposition (SVD).

11 3 A2, B1, C2,

D2 Generalized inverse. Lectures, cooperative

Second Exam

12 3 A1, A2, C1,

C2 Matrix norms, Special kinds of norms, Unitary invariant norms, Condition numbers.

13 3 A2, B1, B3,

D2, C1, C2 Linear squares problem, Quadratic forms.

14 3 B1, B2, B3,

D1 LU -decompositions. Lectures, cooperative

learning and discussion Homework's , Quiz

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and Exams

References:

A.

Main Textbook:

Matrix Theory : Basic Results and Techniques, Zhang F.

B.

Supplementary Textbook(s):

Elementary Linear Algebra, Anton.

The Theory of Matrices, Lancaster P.& Tismenetsky M., 2nd edition Matrix Analysis for Scientists and Engineers, Laub A. J.

Matrix Analysis, Horn R. A.& Johnson C. R.

Assessment Methods:

Methods Grade Date

First Exam 25

Second Exam 25

Final Exam 50

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