• Linear Algebra
    • Department of Mathematics
    • Credit. 3
    • MA077
    • Enroll
    • Fall , 2015
    • 1139
    • Course Description:
    • ( Exchange Programme )
    • This course covers linear equations, matrix theory and vector space, emphasizing topics useful in other disciplines. Linear algebra is a branch of mathematics that studies systems of linear equations and the properties of matrices. The concepts of linear algebra are extremely useful in physics, economics and social sciences, natural sciences, and engineering. Due to its broad range of applications, linear algebra is one of the most widely taught subjects in college-level mathematics. After successfully completing the course, you will have a good understanding of the following topics and their relations: linear systems, matrix theory and vector space.
    • Course Syllabus:
    • After completing the course, students should:
      1. Solving Ax = b for square systems by elimination and determine whether the linear system is consistent or inconsistent by rank of A .
      2. grasp the operations, such as addition, multiplicity, inverse, transpose, of matrix Find the null space and range space, rank of a matrix A.
      3. Linear independence and Linear dependence, basis and dimension of vector space.
      4. Orthogonalization by Gram-Schmidt.
      5. Eigenvalues and eigenvectors. Diagonalization. Symmetric matrices and positive definite matrices,
      6. Properties of determinants
    • Schedule:
    • Topics/ Credit hours / Teaching methodology / Tasks / Intended learning outcomes / Assessment methods

      1.Introduction to matrices and systems of linear equations/2 Credit hours /teaching/6 questions/Grasp /homework
      2.Echelon form and Gouss-Jordan elimination/2 Credit hours /teaching/5 questions /Grasp/ homework
      3.Consistent systems of linear equations and applications/2 Credit hours /teaching/6 questions/ Grasp/homework
      4.Matrix operations. and algebraic properties of matrix operations/2 Credit hours / teaching /7 questions/ Grasp/homework
      5.Linear independence and nonsingular matrices, Matrix inverses and their properties./ 4 Credit hours /teaching/6 questions/Grasp/homework
      6.Introduction and vector space properties of n-dimension vectors/4 Credit hours / teaching/ 5 questions/Grasp/homework
      7.Bases for subspaces./2 Credit hours /teaching/6 questions/Grasp/homework
      8.Dimensions of subspaces of n-dimension vectors./4 Credit hours /teaching/4 questions/ Grasp/ homework
      9.Orthogonal bases for subspaces./2 Credit hours /teaching/5 questions/Grasp/ homework
      10.Definition and properties of determinants./2 Credit hours /teaching/8 questions/ Grasp /homework
      11.Elementary operations and determinants./2 Credit hours /teaching/6 questions/ Grasp/ homework
      12.Cram’s rule and its applications./2 Credit hours /teaching/5 questions/ Grasp/ homework
      13.Eigenvalues and characteristic polynomial./2 Credit hours /teaching/5 questions /Grasp/ homework
      14.Eigenvectors and eigenspaces./2 Credit hours /teaching/5 questions/ Grasp/ homework
      15.Diagonalization and Diagonalization of symmetric matrices./4/teaching/6 questions/Grasp/homework
      16.Definition and basic properties of general vector spaces and subspaces./2 Credit hours /teaching/5 questions/Grasp/homework
      17.Subspaces. Linear independence, Bases and Coordinates/2 Credit hours /teaching/ 6 questions/ Grasp/homework
      18.Dimension, Orthogonal bases and inner product spaces/2 Credit hours /teaching/5 questions/ Grasp/ homework
      19.Definition of quadratic forms and Orthogonal transformation/2 Credit hours / teaching/ 5 questions/ Grasp/homework
      20.Positive definite quadratic forms and positive semidefinite quadratic forms/ 2 Credit hours / teaching/ 5 questions/ Grasp/homework
  • Reading list
  • Other Materials
  • Discussion
  • Homework download/submit
    • Zhang Xiaodong
    • Read more
    • Male
    • E-mail:
    • xiaodong@sjtu.edu.cn
    • Profile
  • Prerequisite Course:

  • Textbooks:

    Introduction to Linear Algebra , fifth edition, by Lee W. Johnson, R. Dean Riess and Jimmy T. Arnold, Pearson Education,.
  • Grading:

    20%--30%/Problem sets
    70%-80%/Final exam
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