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Linear algebra is an important component of undergraduate mathematics. The course content covers fundamental concepts of linear algebra such as solving linear system of equations, vector/matrix algebraic theory, determinant and its properties, vector space, linear transformations, orthogonality, eigenvalues, eigenvectors and applications to linear differential equations, Least squares and projections. With its strong logic, abstract feature and wide applications, linear algebra mainly discusses the linear theory and method of the finite-dimensional linear space. With the fast development of science and technology, there are many problems in Big data, Artificial Intelligence, Cloud calculation etc. concerning the fundamental matrix theory and systems of linear equations.
The famous French mathematician called Rene Descartes said “all problems can be transformed into mathematical problems, and all mathematical problems can be transformed into algebraic problems, and all algebraic problems can be transformed into equations.” Therefore, once the equation problem has been solved, all problems will be solved!
Furthermore, elementary linear algebra is a valuable introduction to mathematical abstraction and logical reasoning because the theoretical development is self-contained, consistent, and accessible to most students.
Thus, after learning this course, you will master not only matrix theory and systems of linear equations, vector space, eigenvalue etc., but also have the ability of matrix operation, matrix methods to solve some practical problems. We hope this course will help you to build the essential mathematics for the study of follow-up courses and other academic subjects, the further broadening of mathematical knowledge and the improvement of mathematical attainment.
Dear students, the main objective of this course is to develop students’ abstract thinking and to train the students’ practical ability.
- master not only matrix theory and systems of linear equations, vector space, eigenvalue etc., but also have the ability of matrix operation, matrix methods to solve some practical problems.
- build the essential mathematics for the study of follow-up courses and other academic subjects.
- develop the further broadening of mathematical knowledge and the improvement of mathematical attainment.
Chapter 1 Systems of Linear Equations
1.1Systems of linear equations
1.2 Gaussian Elimination, Row Echelon Form
1.3 Matrix addition and scale multiplication
1.4 Matrix multiplication
1.5 Transpose of a Matrix
1.6 Matrix Inversion
1.7 Elementary Matrices and its properties
1.8 Inverse Matrix Calculation
1.9 Partitioned Matrices
1.10 Partitioned Diagonal Matrices
unit test 1
Homework for chapter 1
Chapter 2 Determinants
2.1 Definition of the determinant of a matrix
2.2 Properties of determinants
2.3 Computation of determinants
2.4 Finding inverse of a matrix by its adjoint
2.5 Cramer’s Rule and its application
unit test 2
Homework for chapter 2
Chapter 3 Vector Space
3.1 Definitions of vector spaces
3.2 Definitions of subspaces
3.3 Linear independence
3.4 Basis and dimension
3.5 Change of basis
3.6 Solution spaces of linear systems
3.7 Row space and column space of a matrix
Homework for chapter 3
unit test 3
Chapter 4 Linear Transformations
4.1 Definition and Examples
4.2 Matrix Representations of Linear Transformations
4.3 Similarity
unit test 4
Homework for chapter 4
Chapter 5 Orthogonality
5.3 Orthogonal subspaces
5.4 Four fundamental subspaces
5.5 Least squares problems
5.6 Orthogonal sets and orthonormal sets
5.7 The Gram-Schimidt orthogonalization process
5.8 Gram-Schimidt QR factorization
5.9 Orthogonal polynomials and its application
5.10 Applications of scalar product
5.1 The scalar product in Rn
5.2 Inner product spaces
Homework for chapter 5
unit test 5
Chapter 6 Eigenvalues
6.1 Eigenvalues and eigenvectors
6.2 Properties of eigenvalues and eigenvectors
6.3 Systems of Linear Differential Equations
6.4 Diagonalization
6.5 Applications of eigenvalues and eigenvectors
Homework for chapter 6
unit test 6
Calculus 1 and Primary Mathematics
Textbook:
Linear Algebra with Applications (9th Edition), Steven J. Leon, China Machine Press, 2012.
References:
[1] Elementary Linear Algebra (7th Edition), Ron Larson, Cengage Learning, 2012.
[2] Introduction to Linear Algebra (3rd Edition), Gilbert Strang, Wellesley-Cambridge Press, 2003.
[3] Student Guide to Linear Algebra with Applications, ISBN 0-13-600930-1.
[4] A special Web site to accompany the 8th edition: www.pearsonhighered.com/leon
[5] The collection of software tools (M-files) downloaded from the ATLAST Web site: www.umassd.edu/specialprograms/atlast
Associate professor
Professor
assistant professor
