本課程為進階課程，課程著重於廣義向量空間、子空間與內積向量空間的特性及其相關應用，包括：向量空間的同構、向量空間之線性轉移、矩陣反矩陣、函數反函數、矩陣的對角線化、向量的正交性等問題的性質及其相關應用。

To gain a solid concept of linear algebra – theories and applications1. Real Vector Spaces (Review) a. Homogeneous Systems b. Coordinates c. Rank of a Matrix 2. Inner Product Spaces a. Inner Product Spaces (Generalized Cases) b. Gram-Schmidt Process c. Orthogonal Complements 3. Eigenvalues and Eigenvectors a. Eigenvalues and Eigenvectors b. Diagonalization and Similar Matrices c. Diagonalization of Symmetric Matrices 4. Spectral Decomposition and Singular Value Decomposition

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