Linear Algebra

Undergraduate course, Guangdong University of Petrochemical Technology, Computer Department, 2025

Linear algebra is a basic lesson of the advanced mathematics in college education. Also, it provides the fundamental calculating rule to the engineering and information science disciplines.

Moreover, linear algebra plays significate role in most technology and sciences because of calculating efficiently and constructing natural patton to model. Even if the nonlinear models, which is difficultly developed into linear model, there are the differential of a multivariate ways at a fixed area mapped into the best approximate field of the linear functions. Two reference books for learning linear algebra, linear algebra textbook and linear algebra lesson.

Answers to textbook exercises: Chapter 1, Chapter 2, Chapter 3, Chapter 4.

Chapter Date/Slides Tasks Description
Ch1 Determinant 0930 none order 2 and 3 determinant
  1010 none order n determinant
  1010 none properties of determinant
  1014 Exercise1 determinant expansion
  1017 Answer1,homework Cramer formula
Ch2 Matrices 1021, 1024 none Matrix definition and calculation
  1024 Exercise2 Inverse Matrix
  1028 Exam Partitioned matrices
  1031 Answer2 Matrix elementary transformation
  1031 none Matrices rank
Ch3 Linear System 1104, 1107 none Solutions to a system of linear equations
  1111 homework sets of vectors and its linear combination
  1118 none linearly dependent vectors
  1121 Exercise3 rank of a set of vectors
  1125 none structure of solutions to linear systems
  1125 Answer3, homework vector space
Ch4 Normal matrix 1128 Exercise4 dot product
  1202 Answer4 Eigenvalue, eigenvector
  1205 Exercise5 similar matrix
  1209 Answer5 diagonalization
  1212 none quadratic form, standard form
  1216 none positive-define matrix
  1219 LM cheat sheet Review