Linear Algebra (eBook)

Sterling K. Berberian (Autor)

eBook Download: EPUB

2014
384 Seiten
Dover Publications (Verlag)
978-0-486-79503-4 (ISBN)

Infos

Introductory treatment covers basic theory of vector spaces and linear maps — dimension, determinants, eigenvalues, and eigenvectors — plus more advanced topics such as the study of canonical forms for matrices. 1992 edition.

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A thorough first course in linear algebra, this two-part treatment begins with the basic theory of vector spaces and linear maps, including dimension, determinants, eigenvalues, and eigenvectors. The second section addresses more advanced topics such as the study of canonical forms for matrices. The treatment can be tailored to satisfy the requirements of both introductory and advanced courses. Introductory courses that also serve as an initiation into formal mathematics will focus on the first six chapters. Students already schooled in matrices and linear mappings as well as theorem-proving will quickly proceed to selected chapters from part two. The selection can emphasize algebra or analysis/geometry, as needed. Ample examples, applications, and exercises appear throughout the text, which is supplemented by three helpful Appendixes.

Autor

Sterling K. Berberian is Professor Emeritus of Mathematics at the University of Texas at Austin and is the author of several books, including Introduction to Hilbert Space, Fundamentals of Real Analysis, and Measure and Integration.

Inhalt

Part I 1. Vector Spaces 2. Linear Mappings 3. Structure of Vector Spaces 4. Matrices 5. Inner Product Spaces 6. Determinants (2 x 2 and 3 x 3) Part II 7. Determinants (n x n) 8. Similarity (Act 1) 9. Euclidean Spaces (Spectral Theory) 10. Equivalence of Matrices over a PIR 11. Similarity (Act II) 12. Unitary Spaces 13. Tensor Products Appendix A Foundations Appendix B Integral Domains, Factorization Theory Appendix C Weierstrass-Bolzano Theorem Index of Notations Index Errata and Comments

Produkt-Details

• Erscheint lt. Verlag: 1.7.2014
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Maße: 190 x 190 mm
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Schlagworte: advanced • Advanced Topics • Algebra • Analysis • Applications • basic theory of vector spaces and linear maps • Canonical Forms • College • Complex • determinants • eigenvalues • Eigenvectors • Examples • Exercises • First Course • Geometry • introductory • linear algebra • linear algebra introduction • Linear mappings • mathematical reference • Mathematical Theory • Mathematics • matrices • scientists • students and teachers • Textbook
• ISBN-10: 0-486-79503-9 / 0486795039
• ISBN-13: 978-0-486-79503-4 / 9780486795034