# Linear Algebra

• Computer Graphics and Multimedia |
• English

#### Description

This course illustrates the nature of mathematics as a blend of technique, theory, and applications. The important problem of solving systems of linear equations leads to the algebra of matrices, determinants, vector spaces, bases and dimension, linear transformations, and Eigen values. Vector spaces are studied in an abstract setting, examining the concepts of linear independence, span, bases, subspaces, and dimension. There follows a discussion of the association between linear transformations and matrices.

#### Program

Computer Graphics and Multimedia

#### Objectives

• Upon completion of this course, students should be able to:
1. Learn the basic theory of linear algebra through Eigen values.
2. Realize the wide applicability of linear algebra by examining applications.
3. Learn some useful algorithms for linear systems.

#### Textbook

Data will be available soon!

#### Course Content

content serial Description
1â€¢ Classification of Matrixrnâ€¢ Matrix Algebraic Operations â€¢ Define what is meant by Matrixrnâ€¢ Describe types of matrices and its Algebraic operations â€¢ Examine and Evaluate Algebraic operations of Matrices â€¢ Apply the Eigen values and Eigen vectors in applications such as graph Laplacianrn â€¢ Communicate scientific findings in vector spacern
2â€¢ Matrix transpose Determinants â€¢ Define The transpose of Matrixrnâ€¢ Define The Matrix Determinants â€¢ Extract Determinants with different order rn
3rnâ€¢ Matrix inverse â€¢ Describe Matrix Inverse â€¢ Evaluate Matrix Inverse rnâ€¢ Solve square linear system with unique solution using matrix inverse rn
4â€¢ Equivalent matrices â€“ rank of the matrix â€¢ Define Equivalent Matrices rnâ€¢ Define Matrix Rank â€¢ Examine Equivalent Matrices rnâ€¢ Evaluate Matrix Rankrn
5â€¢ Equivalent matrices â€“ rank of the matrix â€¢ Define Equivalent Matrices rnâ€¢ Define Matrix Rank â€¢ Examine Equivalent Matrices rnâ€¢ Evaluate Matrix Rankrn
6rnâ€¢ Consistence of system of linear equations â€¢ Identify consistency of the linear system â€¢ Examine the consistency of the linear system and find its solutionrn
7â€¢ Vector algebra â€¢ Define Vector rnâ€¢ Discuss Vectors Algebraic Operations â€¢ Solve Algebraic operations about vector addition, scalar multiplication, inner products, projections, norms, orthogonal vectorsrn
8â€¢ Eigen values and Eigen vectors â€¢ Define Eigen values and Eigen vectors of a given matrix â€¢ Determine the Eigen values and Eigen vectors of a given matrixrn
9â€¢ Vector space â€¢ Define Vector spacernâ€¢ Describe The characteristics of a Vector Space â€¢ Examine the characteristics of a Vector Space on different problems rnâ€¢ Build a matlab computer program to calculate Gram-Schmidt rnâ€¢ Evaluate numerical stabilityrn rn rn rn rn â€¢ Enlist researchable problemsin the field of linear algebra rnrnrn
10â€¢ Subspaces â€¢ Define The Subspace of a Vector Space â€¢ Examine the Subspace of given problems
11rnâ€¢ Linear independence , The span â€¢ Define linear independence Span rnâ€¢ Describe linear independence vectors , Spanning sets â€¢ Solve algebraic problems about linear independence, spanning setsrn
12â€¢ Basis and Dimension â€¢ Define basis and dimension of a vector space rn â€¢ Determine basis and dimension of abstract vector spaces rn
13â€¢ Orthonormal basis rnâ€¢ Gram-Schmidt process â€¢ Define Orthonormal basis (A.5)rnâ€¢ Describe Gram-Schmidt process â€¢ Apply Gram-Schmidt process to orthogonalize vectorsrn
14rnâ€¢ Linear transformationrnâ€¢ Diagonalization â€¢ Define linear mapping rnâ€¢ Describe Matrix diagonalization â€¢ Examine linear mapsrnâ€¢ Apply diagonalization process rn
15rnGeneral Revisionrn
16

#### Markets and Career

• Generation, transmission, distribution and utilization of electrical power for public and private sectors to secure both continuous and emergency demands.
• Electrical power feeding for civil and military marine and aviation utilities.
• Electrical works in construction engineering.