Learning Outcomes |
PO |
MME |
The students who succeeded in this course: |
|
|
LO-1 |
Can learn the types of some special matrices. |
PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems.
|
Examination |
LO-2 |
Can attain scientific knowledge and study as independent. |
PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other.
|
Performance Project Term Paper |
LO-3 |
Can realize the applications of special matrices and characterizations. |
PO-3 Mathematics, natural sciences and their branches in these areas and related issues has sufficient infrastructure solutions for the problems of theoretical and practical uses of mathematics.
|
Examination |
PO: Programme Outcomes MME:Method of measurement & Evaluation |
Course Contents |
Norms for vectors and matrices, Analytic, algebraic and geometric properties of vector norms, Errors in inverses and solutions of linear system, Location and perturbation of eigenvalues, Gersgorin discs, Perturbation theorems, Positive definite matrices and characterizations, Inequalities for positive definite matrices, Nonnegative matrices and characterizations, Irreducible nonnegative matrices, Stochastic and doubly stochastic matrix. |
Weekly Course Content |
Week |
Subject |
Learning Activities and Teaching Methods |
1 |
Norms for vectors and matrices |
Teaching of Topic and Applications |
2 |
Norms for vectors and matrices |
Teaching of Topic and Applications |
3 |
Analytic, algebraic and geometric properties of vector norms, |
Teaching of Topic and Applications |
4 |
Errors in inverses and solutions of linear system |
Teaching of Topic and Applications |
5 |
Location and perturbation of eigenvalues |
Teaching of Topic and Applications |
6 |
Gersgorin discs |
Teaching of Topic and Applications |
7 |
Perturbation theorems |
Teaching of Topic and Applications |
8 |
mid-term exam |
|
9 |
Positive definite matrices and characterizations |
Teaching of Topic and Applications |
10 |
Positive definite matrices and characterizations |
Teaching of Topic and Applications |
11 |
Inequalities for positive definite matrices |
Teaching of Topic and Applications |
12 |
Nonnegative matrices and characterizations |
Teaching of Topic and Applications |
13 |
Nonnegative matrices and characterizations |
Teaching of Topic and Applications |
14 |
Irreducible nonnegative matrices |
Teaching of Topic and Applications |
15 |
Stochastic and doubly stochastic matrix |
Teaching of Topic and Applications |
16 |
final exam |
|
Recommend Course Book / Supplementary Book/Reading |
1 |
Horn R. A. (1985), Matrix analysis, Cambridge University Press |
2 |
Bronson R. (1989), Matris İşlemleri (Tercüme),Nobel Yayın Dağıtım |
3 |
Serre D. (2010), Matrices: Theory and Applications (Graduate Texts in Mathem atics), Springer (2.Edition) |
Required Course instruments and materials |
The books of lecture. |