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선형대수학 목차 본문

선형대수학

선형대수학 목차

코딩중독 수악중독 2017.04.29 21:32

선형대수학 목차

1. Matrix Operations

2. The Inverse of a Matrix

3. Characterizations of Invertible Matrices

4. Partitioned Matrices

5. Matrix Factorizations

6. The Leontief Input-Output Model

7. Applications to Computer Graphics

8. Subspaces of ${\mathbb R}^n$

1. Introduction to Determinants

2. Properties of Determinants

3. Cramer's Rule, Volume, and Linear Transformations

1. Vector Spaces and Subspaces

2. Null Spaces, Column Spaces, and Linear Transformations

3. Linearly Independent Sets; Bases

4. Coordinate Systems

5. The Dimension of a Vector Space

6. Rank

7. Change of Basis

8. Applications to Difference Equations

9. Applications to Markov Chains

1. Eigenvectors and Eigenvalues

2. The Characteristic Equation

3. Diagonalization

4. Eigenvectors and Linear Transformations

5. Complex Eigenvalues

6. Discrete Dynamical Systems

7. Applications to Differential Equations

8. Iterative Estimates for Eigenvalues

1. Inner Product, Length, and Orthogonality

2. Orthogonal Sets

3. Orthogonal Projections

4. The Gram-Schmidt Process

5. Least-Square Problems

6. Applications to Linear Models

7. Inner Product Spaces

8. Applications of Inner Product Spaces

1. Diagonalization ofSymmetric Matrices

2. Quadratic Forms

3. Constrained Optimization

4. The Singular Value Decomposition

5. Applications to Image Processing and Statistics

1. Affine Combinations

2. Affine Independence

3. Convex Combinations

4. Hyperplanes

5. Polytopes

6. Curves and Surfaces

1. Matrix Games

2. Linear Programming-Geometric Method

3. Linear Programming-Simplex Method

4. Duality

1. Introduction and Examples

2. The Steady-State Vector and Google's PageRank

3. Communication Classes

4. Classification of States and Periodicity

5. The Fundamental Matrix

6. Markov Chains and Baseball Statistics






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