This is supplemental course information, designed to give you a fuller picture of the course and an expanded look at the topics covered. This is an unofficial document. The USC Course Catalog is the binding description of all university courses. Information such as books, materials covered, and the order of topics is subject to change. Please consult instructor for this semseter to get more upto date course information.
Catalog Data:
EE 241 Applied Linear Algebra for Engineering (3, FaSp) Introduction to the theory of matrices, vector spaces, least-squares approximation and MATLAB. Applications to communications, control and signal processing. Prerequisite: MATH 126.
Textbook:
Introductory Linear Algebra by: B. Kolman, 7th Ed.
Recommended: Introduction to Scientific Computing (on MATLAB) by C. F. Van Loan
Coordinator:
Vijay Kumar, Professor of Electrical Engineering
Topics:
1. Linear system of equations, method of elimination.
2. Matrices: addition, transpose, and product. Matrix form of a linear system of equations. Solving a linear system of equations. Reduced row echelon form, Gauss-Jordan method, Homogeneous systems.
3. Determinants. Permutations. Properties of determinant. Geometric significance of determinant. Expansion in cofactors. Inverse of a matrix. Determinants from a computational point of view.
4. Vectors in Rn. Norm. Angle between vectors. Definition of Group. Vector addition and scalar multiplication. Schwartz inequality. Triangle inequality. Linear transformations. Cross product in R3..
5. Lines & Planes in R3. Real vector spaces. Linear combinations. Spanning. Linear independence. Basis. Dimension. Row space. Column space. Rank. Coordinates and change of Basis.
6. Transition matrix. Orthonormal Bases. Gram-Schmidt Orthogonalization. Intersection, union, and sum of subspaces. Projections.
7. Eigenvalues and Eigenvectors. Characteristic equation. Similar matrices. The diagonal form of a matrix.
Course Objectives:
To introduce the student to the mathematical techniques and application skills needed to formulate and solve Linear Algebra problems. Use of matrices and MATLAB is emphasized in the course.
Course Outcomes:
The student will be able to:
1. Solve linear systems of equations.
2. Work with matrices and determinants.
3. Understand real vector spaces, and subspaces.
4. Work with lines and planes in 3-dimensional space.
5. Understand the definitions of spanning, linear independence, and basis.
6. Change a set of basis vectors to an orthonormal basis, and use orthogonal projections.
7. Find Eigenvalues and Eigenvectors and Characteristic equation of a matrix.
8. Understand Similar matrices and the diagonal form of a matrix.
Prepared by: Mostafa Shiva Date: May 20, 2002
