一、課程說明(Course Description)
<br>The course focuses on basic materials and fundamental concepts in linear algebra. 
<br>Topics covered here includes Matrices and Systems of Equations, Determinants, 
<br>Vector Spaces, Linear Transformations, Orthogonality, Eigenvalues and 
<br>Eigenvectors, and Applications of Linear Algebra.
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<br>二、指定用書(Text Books)
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<br>S. H. Friedberg, A. J. Insel, and L. E. Spence, "Linear Algebra," 4th Ed, 
<br>Prentice Hall, 2003
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<br>三、參考書籍(References)
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<br>四、教學方式(Teaching Method)
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<br>4-hour lecture per week
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<br>五、教學進度(Syllabus)
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<br>1. Vector Spaces
<br>   Vector Spaces, Subspaces, Linear Combinations, Linear Equation systems, 
<br>Linear Dependence and Independence, Basis and Dimension
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<br>2. Linear Transformations and Matrices
<br>   Linear Transformation, Null Spaces, Range, Matrix Representation of Linear 
<br>Transformation, Composition of Linear Transformations and Matrix Multiplication, 
<br>Invertibility and Isomorphisms, Change of Coordinate Matrix 
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<br>3. Elementary Matrix Operations and Systems of Linear Equations
<br>   Elementary Matrix Operations and Elementary Matrices, The Rank of a Matrix and 
<br>Matrix Inverses, Systems of Linear Equations
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<br>4. Determinants
<br>   Determinants of order 2 and n, Properties of Determinants
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<br>5. Diagonalization
<br>   Eigenvalues and Eigenvectors, Diagonalizability, Invariant Subspaces and the 
<br>Cayley-Hamilton Theorem
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<br>6. Inner Product Spaces 
<br>   Inner Products and Norms, The Gram-Schmidt Orthogonalization Process, The 
<br>Adjoint of a Linear Operator, Normal and Self-Adjoint Operators, Unitary and 
<br>Orthogonal Operators, Orthogonal Projections and the Spectral Theorem
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<br>六、成績考核(Evaluation)
<br>[Tentative] Midterm Exams (50%), Final Exam (50%)
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<br>七、可連結之網頁位址
<br>The class webpage will be established in the NTHU LMS system
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