Introduction to linear algebra
著者
書誌事項
Introduction to linear algebra
Addison-Wesley, c1998
4th ed
大学図書館所蔵 全4件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes index
内容説明・目次
内容説明
This book stresses both practical computation and theoretical principles and centers on the early introduction of matrix theory and systems of linear equations, elementary vector-space concepts, and the eigenvalue problem. Featuring a gradual increase in the level of difficulty, an accessible writing style, and the integration of MATLAB, this text is an excellent introduction for engineering students.
目次
- 1. Matrices and Systems of Linear Equations. Introduction to Matrices and Systems of Linear Equations. Echelon Form and Gauss-Jordan Elimination. Consistent Systems of Linear Equations. Applications. Matrix Operations. Algebraic Properties of Matrix Operations. Linear Independence and Nonsingular Matrices. Data Fitting, Numerical Integration, and Numerical Differentiation. Matrix Inverses and Their Properties. 2. The Vector Space R^n. Introduction. Vector Space Properties of R^n. Examples of Subspaces. Bases for Subspaces. Dimension. Orthogonal Bases for Subspaces. Linear Transformations from R^n to R^m. Least-Squares Solutions to Inconsistent Systems, with Applications to Data Fitting. Theory and Practice of Least Squares. 3. The Eigenvalue Problem. Introduction. Determinants and the Eigenvalue Problem. Elementary Operations and Determinants. Eigenvalues and the Characteristic Polynomial. Eigenvectors and Eigenspaces. Complex Eigenvalues and Eigenvectors. Similarity Transformations and Diagonalization. Difference Equations
- Markov Chains
- Systems of Differential Equations. 4. Vector Spaces and Linear Transformations. Introduction. Vector Spaces. Subspaces. Linear Independence, Bases, and Coordinates. Dimension. Inner Product Spaces, Orthogonal Bases, and Projections. Linear Transformations. Operations with Linear Transformations. Matrix Representations for Linear Transformations. Change of Basis and Diagonalization. 5. Determinants. Introduction. Cofactor Expansions of Determinants. Cramer's Rule. Applications of Determinants: Inverses and Wronksians. 6. Eigenvalues and Applications. Quadratic Forms. Systems of Differential Equations. Transformation to Hessenberg Matrices. Eigenvalues of Hessenberg Matrices. Householder Transformations. The QR Factorization and Least-Squares Solutions. Matrix Polynomials and the Cayley-Hamilton Theorem. Generalized Eigenvectors and Solutions of Systems of Differential Equations. Appendix A: Introduction to MATLAB. Appendix B: Review of Geometric Vectors.
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