Linear Algebra

 date:2010-1-7 12:10:00          


De'en Gong: Basic Mathematics for Economists --- Linear Algebra, Sichuan People's Publishing House, Sichuan, 2000 (Teaching Material)

Shengwei Qiu: The Lectures of advanced Algebra (part I), Peking University Press, Beijing, 1999

Yizhong Lan: A Course in Summary Linear Algebra, Peking University Press, Beijing, 2002

Structure of the Course:

1.       Determinant

1.1   n-order Determinant

1.2   The Nature of Determinant

1.3   Determinantal Expansion

1.4   Cramer''s Rule

2.       System of linear Eqations

2.1   The elimination method of solving linear equations

2.2   n-dimensional vector group

2.3   The Rank of Vector Collection

2.4   The Rank of Matrix

2.5   General Theory of linear equations group

3.       Matrix

3.1   Matrix Calculations

3.2   Special Matrices

3.3   Partitional Matrices

3.4   Inverse Matrix

3.5   Elementary Matrix

4.       Inner Product of vectors and orthogonal Matrix

4.1   Inner Product of vectors

4.2   Orthogonal Matrix

5.       Proper Value of Matrix and Eigenvector

5.1   Proper Value of Matrix and Eigenvector

5.2   Similarity Matrix and a necessary and sufficient Condition making the Matrix diagonalizable

5.3   The diagonalization of real symmetric Matrix

6.       Quadratic Form

6.1   Quadratic Form and its Matrix

6.2   Normal Form of a quadratic Form

6.3   The Method of transforming quadratic Form into normal Form for a Matrix

6.4   Positive definite Matrix

Course Objectives:

The main purpose of this course is to enable the student to master the basic definition, theory, method and calculation skill of linear algebra by all kinds of teaching method. That makes it possible that student can study other related subsequent courses to become a professional in engineering technology, research and other new science fields. Beyond that, it can also cultivate the student''s ability of abstract, logical, and rational thinking. Then the student has the abilities of analyzing and solving the real problem, and become innovative.


Regular attendance, participation, quizzes, homework: 20%

Mid –Term Test: 40%

Final Test: 40%

Credits & Workload:

3 Credits & 4 hours per Week (teaching) + 2 hours per Week (tutoring); 12 Weeks, 48 hours (teaching) + 24 hours (tutoring)

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