CHAPTER Ⅰ　DETERMINANTS
  §1　Determinants of Order 2 and 3
   1.1　Determinants of order 2
   1.2　Determinants of order 3
   1.3　Exercises
  §2　Determinants of Ordern
   2.1　 Defining by numbers of inverted sequence
   2.2　Defining by induction
   2.3　Exercises
  §3　Properties of Determinants
   3.1　Properties of determinants
   3.2　Examples
   3.3　Exercises
  §4　Cramer’ s Rule
   4.1　Background
   4.2　Cramer’s rule
   4.3　Exercises
 CHAPTER Ⅱ　MATRICES
  §1　Definition of Matrices
   1.1　Definition of a matrix
   1.2　Determinant of a square matrix
   1.3　Transpose of a matrix
   1.4　Exercises
  §2　Addition and Multiplication by a Number
   2.1　Addition of matrices
   2.2　Multiplication of a matrix by a number
   2.3　Calculation rules
   2.4　Exercises
  §3　Multiplication of Matrices
   3.1　Definition of multiplication
   3.2　Calculation rules
   3.3　Unit matrix
   3.4　Powers of square matrices
   3.5　Exercises
  §4　Inverse of a Matrix
   4.1　Inverse of a matrix of order 2
   4.2　Inverse of ann×nmatrix
   4.3　Properties of inverse matrices
   4.4　Exercises
  §5　Elementary Operations of a Matrix
   5.1　Definition of elementary operations
   5.2　Standard form of a matrix
   5.3　Elementary square matrix
   5.4　Find inverse matrices by elementary operations
   5.5　Exercises
  §6　Rank of a Matrix
   6.1　Subdeterminants of a matrix
   6.2　Definition of rank of a matrix
   6.3　Rank and elementary operations
   6.4　Examples
   6.5　Exercises
  §7　Elementary Operations and Elimination
   7.1　Representation of equations by matrices
   7.2　Elimination in simple cases
   7.3　The general case of elimination
   7.4　Systems of homogeneous linear equations
   7.5　Exercises
 CHAPTER Ⅲ　VECTORS
  §1　n-dimensional Vectors
   1.1　Definition ofn-dimensional vectors
   1.2　Linear operations of vectors
   1.3　Vector space
   1.4　Exercises
  §2　Linear Relation among Vectors
   2.1　Linear combination
   2.2　Linear dependence
   2.3　Determining the linear dependence
   2.4　Exercises
  §3　Some Theorems about Linear Dependence
  §4　Rank of a Vector Set
   4.1　Subsets of vectors
   4.2　Definition of the rank
   4.3　Matrix and rank of a vector set
   4.4　Exercises
 CHAPTER Ⅳ STRUCTURE OF SOLUTIONS FOR EQUATIONS
  §1　Homogeneous Equations
   1.1　Properties of solutions
   1.2　Systems of fundamental solutions
   1.3　General solution
   1.4　Exercises
  §2　Nonhomogeneous Equations
   2.1　Structure of solutions
   2.2　Examples
   2.3　Exercises
 CHAPTER Ⅴ　EIGENVALUES
  §1　Similar Matrices
   1.1　Definition of similarity
   1.2　Properties of similar matrices
   1.3　Exercises
  §2　Eigenvalues and Eigenvectors
   2.1　Definition of eigenvalues and eigenvectors
   2.2　Finding eigenvalues and eigenvectors
   2.3　Eigenvalues of similar matrices
   2.4　Exercises
  §3　 Conditions of Translating into a Diagonal Form
   3.1　In the form of eigenvectors
   3.2　In the form of eigenvalues
   3.3　Exercises
  §4　 Eigenvalues and Eigenvectors of a Symmetric Matrix
   4.1　Scalar product of two vectors
   4.2　Orthogonal vector set
   4.3　Orthogonal matrix
   4.4　Eigenvalues and eigenvectors of a real symmetric matrix
   4.5　Exercises
 ANSWERS TO EXERCISES
 INDEX
 REFERENCES