spContent=Linear Algebra is an important subject in applications and theories. It is essential in the following hot technology fields, such as Machine Learning, Big Data and Artificial Intelligence, and fundamental subjects, such as Quantum Mechanics, Multivariate statistics and Differential Equations. The contents studied in Linear Algebra will help you to learn your future courses. You also can enhance your logic thinking ability during the study of this course.
Linear Algebra is an important subject in applications and theories. It is essential in the following hot technology fields, such as Machine Learning, Big Data and Artificial Intelligence, and fundamental subjects, such as Quantum Mechanics, Multivariate statistics and Differential Equations. The contents studied in Linear Algebra will help you to learn your future courses. You also can enhance your logic thinking ability during the study of this course.
—— Instructors
About this course
Linear Algebra is a public basic course for science, engineering and management freshmen. We choose North America popular text book, “Linear Algebra and Its Applications” by David Lay as our text book. If you are planning to study abroad, this course will help you familiar with the material and improve your English. You will learn systems of linear equations, matrices, determinants, vector spaces, eigenvalues and eigenvectors, orthogonality, least squares, symmetric matrices and quadratic forms. The material is different from the linear algebra course in China. It is easy to learn from systems of linear equations that we are familiar with. You will see more informations about linear transformations which will help you understand some essential concepts in linear algebra.
This course is taught by blackboard teaching method which indicate proof process clearly and easy to understand.
Objectives
Learn concepts in linear algebra, such as linear systems, matrices, vector spaces, eigenvectors and eigenvalues, quadratic forms. Master the abilities of solving a linear system, find the rank of a matrix, finding a basis for a vector space, determining if a matrix is diagonalizable. Enhance the logical thinking ability. Have an idea to use linear algebra solve problems in real life.
Syllabus
Linear Equations in Linear Algebra
课时目标：Understand the concepts of Linear systems, vector, linear transformations and linear independence. Know how to solve a linear system, represent the solution set in parametric vector form, determine if a sect of vectors is linearly independent.
1.1 System of Linear Equations
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
1.4 The Matrix Equation Ax =b
1.5 Solution Sets of Linear Systems
1.6 Applications of Linear Systems
1.7 Linear Independence
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation
Matrix Algebra
课时目标：Master matrix operations, such as addition, scalar multiplication, product, inverse. Know the properties of invertible matrices.
2.1 Matrix Operations
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
Determinants
课时目标：Understand the definition of determinants and know how to find the determinant of some types of matrices.
3.1 Introduction to Determinants
3.2 Properties of Determinants
Vector Spaces
课时目标：Understand the concepts of vector space, subspace, column space, row space, null space, bases, dimension, and rank. Know how to find a basis for some vector spaces, find the kernel and range of some linear transformation.
4.1 Vector Spaces and Subspaces
4.2 Null Spaces, Column Spaces and Linear Transformations
4.3 Linearly Independent Sets; Bases
4.4 Coordinate Systems
4.5 The Dimension of a Vector Space
4.6 Rank
4.7 Change of Basis
Eigenvalues and Eigenvectors
课时目标：Understand the concepts of eigenvalues and eigenvectors. Know how to find the eigenvalues and eigenvectors for some matrices, determine a matrix is diagonalizable or not, and can diagonalize it if it is. Can simplify the presentation of a linear transformation.
5.1 Eigenvectors and Eigenvalues
5.2 The Characteristic Equation
5.3 Diagonalization
5.4 Eigenvectors and Linear Transformations
Orthogonality and Least Squares
课时目标：Understand the concepts of inner products, length and orthogonality. Can use the Gram-Schmidt Process to find an orthogonal basis of a vector space. Know how to use the lest-square process deal with the inconsistent linear transformations.
6.1 Inner Product, Length, and Orthogonality
6.2 Orthogonal Sets
6.3 Orthogonal Projections
6.4 The Gram Schmidt Process
6.5 Least-Squares Problems
Symmetric Matrices and Quadratic Forms
课时目标：Know how to diagonalize a symmetric matrix.
7.1 Diagonalization of Symmetric Matrices
7.2 Quadratic Forms
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Prerequisites
References
"Linear Algebra and its Applications", David Lay, 4th ed.
