1. ขอบเขตและเนื้อหารายวิชา Applied Linear Algebra
Matrices and systems of linear equations
- Matrices and Determinants
- Gaussian Elimination, Triangular Factorization
- Theory of Simultaneous Linear Equations
Vector Spaces and Linear Transformations
- Vector Spaces and Subspaces
- Basis, Dimension, Coordinates
- Linear Transformations, Change of Basis and Operation with Matrices
Orthogonal Projections and Least Squares
- Inner Products and Transposes
- Projection onto Subspaces and Least Square Approximations
- Orthogonal Bases and Gram-Schmidt
- The Pseudo-inverse and the Singular Value Decomposition
Eigenvalue Problems
- Determinants, Eigenvalues, Eigenvectors and Eigenspaces
- Similar Transformation and Diagonalization
- Hermitian and Unitary Matrices
- The Jordan Form, Frobenius Form and Schur Form
- Generalized Eigenvalue Problems and Estimation of Eigenvalues
Positive Definite Matrices
- Minima, Maxima, and Saddle Points
- Test for Positive Definiteness
- Semi-definite and Indefinite Matrices
- Minimum Principles and Rayleigh’s Quotient
- The Rayleigh-Ritz Principle
Applications of Linear Algebra
- Application in difference equations and differential equations
- Examples in finite difference and finite element methods
Computation Matrix
- Round-off Errors, Norm and Condition Number of a Matrix
- Iterative Methods for Systems of Linear Equations
- The Computation of Eigenvalues
เอกสารอางอิง
- David C. Lay, Linear Algebra, 3rd edition, Pearson, 2006.
- Howard Anton and Chris Rorres, Elementary Linear Algebra, 9th edition,
Wiley, 2005.
- G. Strang, Linear Algebra and Its Applications, 3rd ed., Thomson Learning,
Inc. 1988.
- G. Golub and C. Van Loan, Matrix Computations, Johns Hopkins Press, 1983.
- P.G. Ciarlet, Introduction to Numerical Linear Algebra and Optimisation,
Cambridge University Press, 1989.
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