Course Contents |
Matrices and matrix operations, Common linear equations, Square matrices, Determinants, Vectors, Eigenvalues and eigenvectors, Matrix funcitons, Canonical basis,Similarity, Inner products, Norms |
Weekly Course Content |
Week |
Subject |
Learning Activities and Teaching Methods |
1 |
Matrices ,Vectors and dot products, Matrix addition and matrix subtraction, |
Teaching topic and applications |
2 |
Scalar multiplication and matrix multiplication, Row-echelon form,Elementary row and column operations, Rank |
Teaching topic and applications |
3 |
Consistency, Matrix notation, Theory of solutions,Simpliflying operations, Gaussian elimination algorthm, Pivoting strategies |
Teaching topic and applications |
4 |
Diagonals, Elementary matrices, LU decomposition,Simultaneous linear equations, Powers of a matrix |
Teaching topic and applications |
5 |
The inverse , Simple inverses, Calculating inverses, Simultaneous linear equations, Properties of the inverse |
Teaching topic and applications |
6 |
Expansion by cofactors, Properties of determinants, Determinants of partitioned matrices,Pivotal condensation, Inversion by determinants |
Teaching topic and applications |
7 |
Dimension,Linear dependence and independence, Linear combinations,Properties of linearly dependent vectors, Row rank and column rank |
Teaching topic and applications |
8 |
mid-term exam |
|
9 |
Characterictic equation, Properties of eigenvalues and eigenvectors, Linearly independent eigenvectors, ,Computational considerations, The Cayley-Hamilton theorem |
Teaching topic and applications |
10 |
Sequences and series of matrices, Well-defined functions,Computing functions of matrices |
Teaching topic and applications |
11 |
The function e, Differentiation and integration of matrices, Differential equations, The matrix equation AX+XB=C |
Teaching topic and applications |
12 |
Generalized eigenvectors,Chains,Canonical basis, The minimum polynomial |
Teaching topic and applications |
13 |
Similar matrices, Modal matrix, Jordan canonical form, Similarty and Jordan canonical form, Functions of matrices |
Teaching topic and applications |
14 |
Complex conjugates, The inner product, Properties of inner products Orthogonality, Gram-Schmidt ortogonalization |
Teaching topic and applications |
15 |
Vector norms, Normalized vectors and distance, Matrix norms, Induced norms, Compatility, Spectral radius |
Teaching topic and applications |
16 |
final exam |
|
Recommend Course Book / Supplementary Book/Reading |
1 |
Matris işlemleri, R.Bronson, Çeviri Editörü: H.H.Hacısalihoğlu, Schaum's outlines,Nobel yayın dağıtım,1989. |
Required Course instruments and materials |
The lecture books |