Linear Algebra Done Right by Sheldon Axler
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About this book :-
This text for a second course in linear algebra is aimed at math majors and graduate students. The novel approach taken here banishes determinants to the end of the book and focuses on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents--without having defined determinants--a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue.
A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus, the text starts by discussing vector spaces, linear independence, span, basis, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite-dimensional spectral theorem. This second edition includes a new section on orthogonal projections and minimization problems. The sections on self-adjoint operators, normal operators, and the spectral theorem have been rewritten. New examples and new exercises have been added, several proofs have been simplified, and hundreds of minor improvements have been made throughout the text.
The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text. The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions.
Book Detail :-
This book has following details information.
Title:
Linear Algebra Done Right by Sheldon Axler by NA
Publisher:
Springer
Series:
freeCompBooks
Year:
2023
Pages:
352
Type:
PDF
Language:
English
ISBN-10 #:
3031410254
ISBN-13 #:
978-3031410253
Country:
Pakistan
License:
CC BY-NC 4.0
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About Author :-
The author NA
NA
Book Contents :-
conver the following topics.
1. Vector Spaces
2. Finite-Dimensional Vector Spaces
3. Linear Maps
4. Polynomials
5. Eigenvalues and Eigenvectors
6. Inner Product Spaces
7. Operators on Inner Product Spaces
8. Operators on Complex Vector Spaces
9. Multilinear Algebra and Determinants
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