LINEAR ALGEBRA

BTS513

Course Code: BTS513
Semester: -
Theory+Practice: 3 + 0
ECTS: 10

Course Type

Elective Course

Course Level

Master's Degree With Thesis

Year of Study

Semester

ECTS

Name of Lecturer(s)

Learning Outcomes

At the end of this course, the students;

will have learned canonical matrix representations of linear operators on finite dimensional vector spaces over arbitrary fields.

Mode of Delivery

Face to face

Prerequisites

Recommended Optional Programme Components

There is no recommended optional programme component for this course.

Course Description

Matrices and determinants. Systems of linear equations. Vector spaces, bases and dimensions. Linear transformations, change of bases. Inverses of a linear transformations. Isomorphism. Eigenvalues and eigen vectors, Jordan normal form. İnner and cross products, orthogonality, quadratic forms, normed spaces

Course Contents

WEEK	TOPICS
1^st Week	Eigenvalues and Eigenvectors
2^nd Week	Diagonalization
3^rd Week	Normal form of Polynomial matrices.
4^th Week	Equivalence of Characteristic Matrices and Similarity.
5^th Week	Rational and Jordan Canonical Forms.
6^th Week	Diagonalizable Complex Matrices.
7^th Week	Real Symmetric Matrices,Hermitian Matrices,Positive Matrices.
8^th Week	MIDTERM
9^th Week	Unitary and Orthogonal Matrices,Reduction of Quadratic Forms,Orthogonal Similarity.
10^th Week	İner products,Norm and Orthogonality,Matrix Forms of İner Products.
11^th Week	Orthogonal and Orthonormal Bases. Orthogonal Projections.
12^th Week	The Gram - Schmidt Orthogonalization Process. The Method of Least Squares.
13^th Week	Linear operators and their adjoints on İnner Product Spaces.
14^th Week	Linear Functionals on İnner Product Spaces.

Programme Qualifications / Learning Outcomes

	LO1
K1	X
K2
K3
K4
K5	X
K6	X
K7
K8	X
K9	X
K10	X
K11