Lesson plan / LINEAR ALGEBRA

Lesson Information

Course Credit 3.0
Course ECTS Credit 5.0
Teaching Language of Instruction İngilizce
Level of Course Bachelor's Degree, TYYÇ: Level 6, EQF-LLL: Level 6, QF-EHEA: First Cycle
Type of Course Compulsory
Mode of Delivery Face-to-face
Does the course require compulsory or optional work experience? Z
Course Coordinator
Instructor (s) Assist. Prof. Dr. NECİP GÖKHAN KASAPOĞLU|Prof. Dr. ÇİĞDEM GENCER BALBİANİ
Course Assistant

Purpose and Content

The aim of the course This module aims to provide information which covers an introduction to linear algebra.
Course Content Matrices, matrix algebra, special types of matrices, elementary row and colon operations, echelon form, rank of a matrix, elementary matrices, inverses, equivalent matrices, determinants, properties of determinants, cofactor and adjoint of a matrix, derivation of inverse matrix, systems of linear equations, solutions of systems of linear equations, Cramer's method, Gauss’s elimination method, vector spaces, subspaces, linear independence, bases and dimension, coordinates, change of basis, inner product spaces, standard inner product, orthogonal subspaces, orthogonal complement of a subspace, inner product, inner product spaces, orthogonal basis, orthogonal matrices, Gram-Schmidt orthogonalization methods, linear transformations, matrix representations of linear transformations, eigen values, eigen vectors, diagonalization, Cayley-Hamilton’s Theorem, quadratic forms, Hermitian forms, numerical applications.

Weekly Course Subjects

1Matrices, matrix algebra, special types of matrices, elementary row and colon operations.
2Echelon form, rank of a matrix, elementary matrices, inverses, equivalent matrices.
3Determinants, properties of determinants, cofactor and adjoint of a matrix.
4Systems of linear equations, solutions of systems of linear equations.
5Cramer's method, Gauss’s elimination method.
6Vector spaces, subspaces, linear independence. Bases and dimension, coordinates, change of basis.
7Inner product spaces, standard inner product function, orthogonal subspaces, orthogonal matrices, orthonormal basis.
8Midterm Exam.
9Gram-Schmidt orthogonalization methods , orthogonal subspaces, orthogonal complement of a subspace.Midterm Exam.
10Linear transformations, rank and kernel of linear transformations.
11Matrix representations of linear transformations.
12Eigen values, eigen vectors, diagonalization.
13Cayley-Hamilton’s Theorem, quadratic forms, Hermitian forms.
14Numerical applications.

Resources

1.Hacısalihoğlu, H. H., Lineer Cebir I, Bilim Yayınları, Ankara, 2000.
2.S. J. Leon, "Linear Algebra with Applications", Prentice Hall, 2002, Sixth Edition.
3. S. Lipschutz, Theory and Problems of Linear Algebra , Schaum’s Outline of McGraw-Hill Book Co.,1987,Singapore.