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XuetangX

Linear Algebra

Swinburne University of Technology via XuetangX

Overview

  Our course is at the late-freshman levelstresses both practical computation and theoretical principles and centers on the principal topics: matrix theory, determinants, systems of linear equations, elementary vector space concepts, and the eigenvalue problem.

  On completion of this course, the student will be able to: solve systems of linear equations and demonstrate an understanding of the nature of the solutions, perform accurate and efficient calculations with vectors, matrices, eigenvalues and eigenvectors in arbitrary dimensions, demonstrate a geometrical understanding of vectors and vector operations in 2 and 3 dimensions, demonstrate an understanding of orthogonality.



Syllabus

  • CHAPTER 1 MATRICES AND SYSTEMS OF EQUATIONS
    • 1.1 SYSTEM OF LINEAR EQUATIONS
    • 1.2 ROW ECHELON FORM
    • 1.3 MATRIX ARITHMETIC AND MATRIX ALGEBRA
    • 1.4 ELEMENTARY MATRICES
    • 1.5 PARTITIONED MATRICES
  • CHAPTER 2 DETERMINANTS
    • 2.1 THE DETERMINANT OF A MATRIX
    • 2.2 PROPERTIES OF DETERMINANTS
    • 2.3 ADDITIONAL TOPICS AND APPLICATIONS
  • CHAPTER 3 VECTOR SPACE AND LINEAR TRANSFORMATIONS
    • 3.1 DEFINITIONS AND EXAMPLES
    • 3.2 SUBSPACES
    • 3.3 LINEAR INDEPENDENCE
    • 3.4 BASIS AND DIMENSION
    • 3.5 CHANGE OF BASIS
    • 3.6 ROW SPACE AND COLUMN SPACE
  • CHAPTER 4 EIGENVALUES AND QUADRATIC FORMS
    • 4.1 EIGENVALUES AND EIGENVECTORS
    • 4.2 DIAGONALIZATION
    • 4.3 DIAGONALIZATION OF SYMMETRIC MATRICES
    • 4.4 QUADRATIC FORMS
  • TEST

    Taught by

    Na HU, Feng ZHOU, Chongyang JIN, Yuan LI, Xiaoming SU, and Na YI

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