Mathematical Economics

  1. Linear Models and Matrix Algebra
    1. Vectors and Vector Spaces
      1. Definition of Vectors
        1. Vectors as Ordered n-tuples
          1. Geometric Representation
            1. Vector Notation
            2. Vector Operations
              1. Vector Addition and Subtraction
                1. Scalar Multiplication
                  1. Dot Product
                    1. Vector Norms
                    2. Vector Spaces
                      1. Definition and Properties
                        1. Subspaces
                          1. Linear Combinations
                        2. Matrices and Matrix Operations
                          1. Definition of Matrices
                            1. Matrix Notation and Dimensions
                              1. Elements and Indexing
                              2. Matrix Operations
                                1. Matrix Addition and Subtraction
                                  1. Scalar Multiplication
                                    1. Matrix Multiplication
                                      1. Properties of Matrix Operations
                                      2. Special Types of Matrices
                                        1. Identity Matrix
                                          1. Null Matrix
                                            1. Diagonal Matrix
                                              1. Upper and Lower Triangular Matrices
                                                1. Transpose of a Matrix
                                                  1. Symmetric Matrices
                                                    1. Skew-Symmetric Matrices
                                                  2. Linear Independence and Rank
                                                    1. Linear Independence of Vectors
                                                      1. Linear Dependence
                                                        1. Basis and Dimension
                                                          1. Rank of a Matrix
                                                            1. Row Rank and Column Rank
                                                              1. Rank-Nullity Theorem
                                                              2. Applications to Economic Systems
                                                              3. Determinants
                                                                1. Definition and Calculation of Determinants
                                                                  1. Properties of Determinants
                                                                    1. Minors and Cofactors
                                                                      1. Expansion by Minors
                                                                        1. Geometric Interpretation
                                                                          1. Cramer's Rule
                                                                            1. Application to Systems of Linear Equations
                                                                              1. Conditions for Applicability
                                                                            2. Matrix Inversion
                                                                              1. The Inverse of a Matrix
                                                                                1. Methods for Finding the Inverse
                                                                                  1. Adjugate Method
                                                                                    1. Gaussian Elimination
                                                                                      1. Elementary Row Operations
                                                                                      2. Conditions for Nonsingularity
                                                                                        1. Properties of Matrix Inverses
                                                                                        2. Systems of Linear Equations
                                                                                          1. Solving Systems of Linear Equations
                                                                                            1. Gaussian Elimination
                                                                                              1. Matrix Methods
                                                                                                1. Existence and Uniqueness of Solutions
                                                                                                2. Homogeneous vs. Nonhomogeneous Systems
                                                                                                  1. Applications to Economic Models
                                                                                                  2. Input-Output Models
                                                                                                    1. Structure of Input-Output Tables
                                                                                                      1. Technology Matrix
                                                                                                        1. Final Demand Vector
                                                                                                          1. Solution of Input-Output Systems
                                                                                                            1. Economic Interpretation
                                                                                                              1. Leontief Inverse

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                                                                                                            2. Static Equilibrium Analysis

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                                                                                                            4. Comparative Static Analysis