Jonathan S. Golan

The Linear Algebra a Beginning Graduate Student Ought to Know (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer-Verlag GmbH
• Seitenzahl: 436
• Erscheinungstermin: 5. April 2007
• Englisch
• ISBN-13: 9781402054952
• Artikelnr.: 43729501

Inhaltsangabe

Notation and terminology.- Fields.- Vector spaces over a field.- Algebras over a field.- Linear independence and dimension.- Linear transformations.- The endomorphism algebra of a vector space.- Representation of linear transformations by matrices.- The algebra of square matrices.- Systems of linear equations.- Determinants.- Eigenvalues and eigenvectors.- Krylov subspaces.- The dual space.- Inner product spaces.- Orthogonality.- Selfadjoint Endomorphisms.- Unitary and Normal endomorphisms.- Moore-Penrose pseudoinverses.- Bilinear transformations and forms.- Summary of Notation.-Index to thumbnail photos.

Rezensionen

From the reviews of the third edition:

"This edition is enhanced by the inclusion of further results and many new examples. There are also over 130 additional exercises and many of the earlier ones have been revised. Furthermore, many more biographical notes and thumbnail portraits of mathematicians connected in some way with linear algebra have been added. This book continues to be very successful and useful, not only as a textbook for advanced linear algebra courses, but also for self-study and reference purposes." (Rabe von Randow, Zentralblatt MATH, Vol. 1237, 2012)