Elementary Linear Algebra, 7/e (IE-Paperback)

Ron Larson

  • 出版商: Cengage Learning
  • 出版日期: 2012-04-01
  • 售價: $1,150
  • 貴賓價: 9.8$1,127
  • 語言: 英文
  • 頁數: 448
  • 裝訂: Paperback
  • ISBN: 1133111343
  • ISBN-13: 9781133111344
  • 相關分類: 線性代數 Linear-algebra

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1. SYSTEMS OF LINEAR EQUATIONS

  • 1.1  Introduction to Systems of Equations.

  • 1.2  Gaussian Elimination and Gauss-Jordan Elimination.

  • 1.3  Applications of Systems of Linear Equations.

2. MATRICES.

  • 2.1  Operations with Matrices.

  • 2.2  Properties of Matrix Operations.

  • 2.3  The Inverse of a Matrix.

  • 2.4  Elementary Matrices.

  • 2.5  Applications of Matrix Operations.

3. DETERMINANTS.

  • 3.1  The Determinant of a Matrix.

  • 3.2  Evaluation of a Determinant Using Elementary Operations.

  • 3.3  Properties of Determinants.

  • 3.4  Applications of Determinants.

4. VECTOR SPACES.

  • 4.1  Vectors in Rn.

  • 4.2  Vector Spaces.

  • 4.3  Subspaces of Vector Spaces.

  • 4.4  Spanning Sets and Linear Independence.

  • 4.5  Basis and Dimension.

  • 4.6  Rank of a Matrix and Systems of Linear Equations.

  • 4.7  Coordinates and Change of Basis.

  • 4.8  Applications of Vector Spaces.

5. INNER PRODUCT SPACES.

  • 5.1  Length and Dot Product in Rn.

  • 5.2  Inner Product Spaces.

  • 5.3  Orthogonal Bases: Gram-Schmidt Process.

  • 5.4  Mathematical Models and Least Squares Analysis.

  • 5.5  Applications of Inner Product Spaces.

6. LINEAR TRANSFORMATIONS.

  • 6.1  Introduction to Linear Transformations.

  • 6.2  The Kernel and Range of a Linear Transformation.

  • 6.3  Matrices for Linear Transformations.

  • 6.4  Transition Matrices and Similarity.

  • 6.5  Applications of Linear Transformations.

7. EIGENVALUES AND EIGENVECTORS.

  • 7.1  Eigenvalues and Eigenvectors.

  • 7.2  Diagonalization.

  • 7.3  Symmetric Matrices and Orthogonal Diagonalization.

  • 7.4  Applications of Eigenvalues and Eigenvectors.

8. COMPLEX VECTOR SPACES (online).

  • 8.1  Complex Numbers.

  • 8.2  Conjugates and Division of Complex Numbers.

  • 8.3  Polar Form and Demoivre's Theorem.

  • 8.4  Complex Vector Spaces and Inner Products.

  • 8.5  Unitary and Hermitian Spaces.

9. LINEAR PROGRAMMING (online).

  • 9.1  Systems of Linear Inequalities.

  • 9.2  Linear Programming Involving Two Variables.

  • 9.3  The Simplex Method: Maximization.

  • 9.4  The Simplex Method: Minimization.

  • 9.5  The Simplex Method: Mixed Constraints.

10. NUMERICAL METHODS (online).

 

  • 10.1  Gaussian Elimination with Partial Pivoting.

  • 10.2  Iterative Methods for Solving Linear Systems.

  • 10.3  Power Method for Approximating Eigenvalues.

  • 10.4  Applications of Numerical Methods.