Course Overview
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Course Synopsis
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This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, eigenvalues, Norms of Vectors and Matrices, Error Bounds and Iterative Refinement, Householder’s Method and QR Algorithum, Singular Value Decomposition, Fixed Points for Functions of Several Variables, Newton’s Method, Quasi-Newton Method.
The goals of this subject are, how we can use Linear Algebra and its numerical applications in different advance fields.
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Course Learning Outcomes
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Upon completing this course students should be able :
- To master the techniques for solving systems of linear equations.
- To introduce matrix algebra as a generalization of single-variable algebra of high school.
- To build on the background in Euclidean space and formalize it with vector space theory.
- To relate linear methods to other areas of mathematics such as calculus and differential equations.
- To develop an appreciation for how numerical linear methods are used in advanced applications.
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Course Calendar
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1
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Introduction and overview
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2
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Introduction to Matrices
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3
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Systems of Linear Equations
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4
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Row Reduction and Echelon Forms
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5
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Null Spaces, Column Spaces, and Linear Transformations
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6
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Linearly Independent Sets; Bases
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9
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Solution of Linear System of Equations (Jacobi Method)
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10
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Solution of Linear System of Equations (Gauss–Seidel Iteration Method)
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11
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Solution of Linear System of Equations (Relaxation Method)
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12
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Norms of Vectors and Matrices, Matrix Norms and Distances
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13
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Error Bounds and Iterative Refinement
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14
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Eigenvalues and Eigenvectors
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15
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The Characteristic Equation
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18
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Orthogonal and Orthonormal set
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19
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Orthogonal Decomposition
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20
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Orthogonal basis, Gram-Schmidt Process, Orthonormal basis
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21
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Least Square Solutions
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22
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Eigen Value Problems (Power Method)
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23
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Eigen Value Problems (Jacobi’s Method)
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24
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Eigen Value Problems (continued)
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26
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Applications of inner product spaces
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27
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Householder’s Method and QR Algorithum
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28
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Singular Value Decomposition
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29
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Fixed Points for Functions of Several Variables
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