School of Humanities \ Mathematics
Course Credit
ECTS Credit
Course Type
Instructional Language
Programs that can take the course
Faculty of Engineering Departments
This course includes the following topics:
Matrices, Elementary Line and Column Operations, Solutions of Linear Equation Systems, Determinants, Vector Spaces, Inner Product Spaces, Linear Transforms, Eigenvalues and Eigenvectors, Diagonalization.
Textbook and / or References
Course Book:
Elementary Linear Algebra, 9th edition, Bernard Kolman and David R. Hill; Prentice Hall, 2004.
References:
Intoduction to Linear Algebra, 3rd edition, Gilbert Strang, Wellesley-Cambridge, 2003
To learn elementary operations and matrices while understanding their algebraic properties. To develop a clear understanding of vectors and vector spaces.
1. Acquires fundamental mathematical knowledge and applies it across different disciplines.
2. Solves systems of linear equations using elementary operations and matrices, analyzing matrices through their characteristic properties.
3. Understands real vector spaces, the concept of inner product, and their geometric and algebraic interpretations.
4. Analyzes linear transformations and represents them using matrix notation.
5. Computes eigenvalues and eigenvectors of a matrix to analyze the dynamic behavior of systems.
6. Diagonalizes matrices to simplify computations.
Week 1: Systems of Linear Equations
Week 2: Matrices, Matrix Operations and Algebraic Properties. Equilon Form
Week 3: Finding solutions of systems of equations. Rank of a matrix. LU factorization of a matrix. System solution with LU factorization. Finding the inverse of a matrix with LU factorization. Determinant calculation with LU factorization
Week 4: Finding the inverse of a matrix using elementary operations
Week 5: Determinant and its properties
Week 6: Cofactor Expansion. Inverse of a matrix
Week 7: Other applications of determinants
Week 8: Vector Spaces, Subvector Spaces, Inner Product Spaces. Linear Independence and Stretching. Base Dimension
Week 9: Eigenvalue, Eigenvector
Week 10: Diagonalization Cayley-Hamilton Method
Week 11 Linear Transformation
Week 12: Kernel in Linear Transformations. 1-1 Linear transformations
Tentative Assesment Methods
• Midterm 40 %
• Final 60 %
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