# COURSE UNIT TITLE

: LINEAR ALGEBRA

#### Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
EED 1008 LINEAR ALGEBRA COMPULSORY 3 0 0 4

#### Offered By

Electrical and Electronics Engineering

#### Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

#### Course Coordinator

ASSOCIATE PROFESSOR DAMLA GÜRKAN KUNTALP

#### Offered to

Electrical and Electronics Engineering

#### Course Objective

To teach the fundamentals and main methods and techniques of linear algebra.

#### Learning Outcomes of the Course Unit

 1 To be able to use and express the fundamental concepts of linear algebra 2 To be able to operate with matrices and vectors 3 To be able to derive the row echelon form, rank of matrices 4 To be able to analyze consistence of the system of linear algebraic equations and find solutions of the systems 5 To be able to reduce quadratic form to sum of squares in principal axes 6 To be able to find eigenvalues and corresponding to them. eigenvectors of matrices 7 To be able to solve linear equation systems

Face -to- Face

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#### Course Contents

 Week Subject Description 1 Matrix Algebra: addition, multiplication by scalar, multiplication of matrices, transpose matrix. 2 Elementary row operations, row-echelon matrices; the algorithm of the reduction of a matrix to REM; examples, rank of matrix. 3 System of linear algebraic equations, consistent and inconsistent systems. Gaussian elimination method for solving linear algebraic systems. System with infinite number of solutions, properties of solutions 4 The inverse of a square matrix, main properties of the inverse matrix; procedure of computing the inverse matrices 5 Permutations, even and odd permutations. The determinant of the square matrix, properties. Minor and cofactor of the matrix, expansion of the determinant, Midterm 1 6 Adjoin matrix, properties of adjoin matrix. Cramer s rule for solving the linear algebraic system 7 Vector spaces, axioms of the vector space, examples. Subspaces, spanning sets, span; linear dependence and linear independence of vectors and functions 8 Eigenvalues and eigenvectors of the square matrix, solving eigenvalue-eigenvector problems. Finding eigenspaces 9 Defective and non-defective matrices, similarity of matrices, diagonalizable matrices 10 Inner product, Cauchy-Schwarz inequality; orthogonal and orthonormal sets of vectors, Gram-Schmidt orthogonalization procedure. Basis and dimension of the space 11 Midterm II, The cross product in three dimensional space, norm of the cross product 12 Symmetric matrix: properties, diagonalization by orthogonal matrix 13 Quadratic forms, reduction of the quadratic form to a sum of squares, principal axes 14 Transformations of vector spaces. Structure of linear transformations. Examples of the linear transformations: the rotation and the reflection in two dimensional spaces

Ana kaynak: Goode S.W., Differential Equations and Linear Algebra, Prentice Hall, New Jersey, 2002 Chapters 3,4,5,6

Yardımcı kaynaklar: Piziak R. and Odell P.L., Matrix Theory, Baylor University, Texas, 2007

Goldberg J.L., Matrix theory with applications, McGraw-hill, New York, 1992

Referanslar:
Diğer ders materyalleri: PDF files of lecture notes of Prof. Dr. Valery Yakhno

Lectures
Homeworks
Examinations

#### Assessment Methods

 SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE1 MIDTERM EXAM 1 2 MTE2 MIDTERM EXAM 2 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE MTE1 * 0.25 + MTE2 * 0.25 + FIN * 0.50 5 RST RESIT 6 FCG FINAL COURSE GRADE MTE 1 * 0.25 + MTE 2 * 0.25 + RST * 0.50

*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

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Sınavlar

English

To be announced.

#### Contact Details for the Lecturer(s)

damla.kuntalp@deu.edu.tr
02323017166

To be announced.

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