The Linear Algebra a Beginning Graduate Student Ought to Know için kapak resmi
Başlık:
The Linear Algebra a Beginning Graduate Student Ought to Know
Dil:
English
ISBN:
9781402054952
Yayın Bilgileri:
Dordrecht : Springer Netherlands, 2007.
Fiziksel Tanımlama:
XII, 436 p. online resource.
İçerik:
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.
Özet:
Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as computer science, the physical and social sciences, and engineering. It entails an extensive corpus of theoretical results as well as a large body of computational techniques. The book is intended to be used in one of several possible ways: (1) as a self-study guide; (2) as a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level; or (3) as a reference book. It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams. The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some basic ideas and techniques, such as the solution of a small system of linear equations over the real numbers. More importantly, it does assume a seriousness of purpose and a modicum of mathematical sophistication. The book also contains over 1000 exercises, many of which are very challenging.

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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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The title of this book is fully descriptive: Golan (Univ. of Haifa, Israel) feels that although algebra continues to be a component of undergraduate education, the standard undergraduate course no longer adequately prepares students in mathematics, engineering, sciences, and social sciences for the appropriate understanding and use of linear algebra required by those disciplines. This book is intended to fill that gap. Though it could be used as a resource in an advanced linear algebra course, it is more likely to be used for self-study or reference. For that intended use, the book is self-contained and starts from first principles; and for the intended audience, its style is mature and mathematically correct as opposed to being expository. Golan takes an active learning approach by including almost 1,000 exercises spread among the chapters. He also attempts to tie theoretical linear algebra to computational uses. Although access to computer algebra software is not required, it is recommended. No bibliography, but extensive historical notes throughout. ^BSumming Up: Recommended. Upper-division undergraduate and graduate students; professionals. D. Z. Spicer University System of Maryland