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

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

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。

This course is an advanced course. The course focuses on the characteristics and related applications of broad vector space, subspace and internal vector space, including: the synonym of vector space, linear shift of vector space, matrix inverse function, function inverse function, the angular linearization of matrix, vector orthogonality and other problems.

Elementary Linear Algebra With Applications by Bernard Kolman & David R. Hill ISBN-13 : 978-0-13-135063-2
Linear Algebra: A Modern Introduction by David Pooles ISBN-13: 978-0538735452
Linear Algebra by Stephen H. Friedberg, Arnold J. Insel, & Lawrence E. Spence ISBN-13: 978-0130084514
Linear Linear Algebra With Applications by Gareth Williams ISBN-13: 978-1449679545
Linear Algebra: An Introduction Richard Bronson by Gabriel B. Costa ISBN-13: 978-0120887842
Elementary Linear Algebra with Applications by Howard Anton & Chris Rorres ISBN-13: 978-0471669593
Linear Algebra by Kenneth & Kunze & Ray Hoffman ISBN-13: 978-8120302709

Elementary Linear Algebra With Applications by Bernard Kolman & David R. Hill ISBN-13 : 978-0-13-135063-2
Linear Algebra: A Modern Introduction by David Pooles ISBN-13: 978-0538735452
Linear Algebra by Stephen H. Friedberg, Arnold J. Insel, & Lawrence E. Spence ISBN-13: 978-0130084514
Linear Linear Algebra With Applications by Gareth Williams ISBN-13: 978-1449679545
Linear Algebra: An Introduction Richard Bronson by Gabriel B. Costa ISBN-13: 978-0120887842
Elementary Linear Algebra with Applications by Howard Anton & Chris Rorres ISBN-13: 978-0471669593
Linear Algebra by Kenneth & Kunze & Ray Hoffman ISBN-13: 978-8120302709