Linear Algebra Lecture Notes
by Ling-Hsiao Lyu / lyu@jupiter.ss.ncu.edu.tw

Citation: Lyu, L. H. (2012), Linear Algebra Lecture Notes,
http://www.ss.ncu.edu.tw/~lyu/lecture_files_en/lyu_LA_Notes/lyu_LA_Content.html

Table of Contents

Lecture 1. Introduction to Linear Algebra and Matrix Operations

Lecture 2. General Solution of Ax=b_and Vector Space

Additional Lecture Notes for Lectures 2 and 3 (total 10 pages)

Lecture 3. Projection and Projection Matrix

Lecture 4. Least Squares Fit (LSF):_Approximate Solution of Ax=b

Lecture 5. Determinant

Lecture 6. Change of Basis

Understand the physical meaning of the eigen vectors (or, the principle axis) of an anisotropic rotational inertia (轉動慣量, or moment of inertia), I.
YouTube - Rotating Solid Bodies in Microgravity

YouTube - Richard Garriott Space Video Blog: Rotational Inertia

YouTube - Richard Garriott Space Video Blog: Gyroscopes

YouTube - Moment of Inertia Explained

Lecture 7. Eigenvalues and Eigenvectors

7a. Eigenvalue and Eigenvector -- A Case Study
7b. Eigenvalue and Eigenvector -- A General Discussion
7c. Introduction to Positive Definite Matrices, Similar Matrices, Jorden Form, & Singular Value Decomposition (SVD)

Textbook:

• Strang, G., Introduction to Linear Algebra, International edition, Wellesley-Cambridge Press, Wellesley, 2005.
• Leon, S. J., Linear Algebra with Applications, 8th edition, Pearson Prentice Hall, Pearson Education Inc., New Jersey, 2010.
• List of all lectures given by Professor Strang in Spring 2005
  
  LinearAlgebraVideoLectures.doc
  
  LinearAlgebraVideoLectures.pdf
  

Reference Books:

• Mathews, J., and R. L. Walker, Mathematical Methods of Physics, 2nd edition, Chapter 6, New York, 1970.
• Paige, L. J., and J. D. Swift, Elements of Linear Algebra, Blaisdell Publ. Co., New York, 1961.
• Hoffman, K., and R. Kunze, Linear Algebra, Prentice-Hall, Inc., New Jersey, 1971.
• Fraleigh, J. B., and R. A. Beauregard, Linear Algebra, 3rd edition, Addison Wesley, New York, 1995.
• Johnson, E. W., R. D. Riess, and J. T. Arnold, Introduction to Linear Algebra, 5th edition, Addison Wesley, New York, 2002.
• Willians, G., Linear Algebra With Application, 6th edition, Jones and Bartlett Publ., Landon, 2008.