The Linear Algebra - A Beginning Graduate Student Ought to Know （2ND）

The Linear Algebra - A Beginning Graduate Student Ought to Know （2ND）

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  • 製本 Hardcover:ハードカバー版／ページ数 405 p.
  • 言語 ENG
  • 商品コード 9781402054945
  • DDC分類 512

基本説明

Deals rigorously with the abstract theory and, at the same time, devotes considerable space to the numerical and computational aspects of linear algebra.

Full Description


This book rigorously deals with the abstract theory and, at the same time, devotes considerable space to the numerical and computational aspects of linear algebra. It features a large number of thumbnail portraits of researchers who have contributed to the development of linear algebra as we know it today and also includes over 1,000 exercises, many of which are very challenging. The book can be used as a self-study guide; a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level; or as a reference book.

Contents

1. Notation and terminology.- 2. Fields.- 3. Vector spaces over a field.- 4. Algebras over a field.- 5. Linear Dependence and Dimension.- 6. Linear Transformations.- 7. The endomorphism algebra of a vector space.- 8. Representation of linear transformations by matrices.- 9. The algebra of square matrices.- 10. Systems of linear equations.- 11.Determinants.- 12. Eigenvalues and eigenvectors.- 13. Krylov subspaces.- 14. The dual space.- 15. Inner product spaces.- 16. Orthogonality.- 17. Selfadjoint endomorphisms.- 18. Unitary and normal endomorphisms.- 19. Moore-Penrose pseudoinverses.- 20. Bilinear transformations and forms.