Linear Algebra
Will be published approx. on 17. May 2021
Book
Paperback/Softback
172 pages
978-1-7924-6399-0 (ISBN)
Description
This book is intended as a textbook for a one-term undergraduate second linear algebra course which prepares students for both applied mathematics and pure mathematics, in particular, for Galois Theory. The students are assumed to have some knowledge on calculus, linear systems, determinates and matrices. Earlier drafts of this book have been used as the textbook when the author teaches MA222, the second linear algebra course of the three, at Wilfrid Laurier University since 2019.The book contains 196 exercises of varying difficulty which will allow students to practice their own computational and proof-writing skills. Detailed solutions, answers or hints to all the exercises are provided in the book. Besides standard ones, many of the exercises are provided in the book. Besides standard ones, many of the exercises are interesting. Some are rather hard. It is not a surprise if the reader cannot solve some of the exercises by themselves, particularly for first learners. It is strongly suggested that the readers first try to solve them without looking at the solutions of hints.
More details
Language
English
Place of publication
Iowa
United States
Target group
College/higher education
Dimensions
Height: 276 mm
Width: 214 mm
Thickness: 11 mm
Weight
422 gr
ISBN-13
978-1-7924-6399-0 (9781792463990)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Content
- 1. Complex Numbers, Polynomials Over a Field
- 1.1 Arithmetic of complex numbers
- 1.2 Polar form of complex numbers
- 1.3 Polynomials over a field
- 1.4 Irreducible polynomials
- 1.5 Exercises
- 2. Determinants
- 2.1 Evaluating determinants
- 2.2 Exercises
- 3. Vector Spaces and Subspaces
- 3.1 Basic properties of vector spaces
- 3.2 Subspaces
- 3.3 Spanning sets and linear dependence
- 3.4 Bases and dimension
- 3.5 Applications and Sum-Dimension Formula
- 3.6 Quotient spaces
- 3.7 Exercises
- 4. Linear Maps
- 4.1 Linear maps, Dimension Theorem
- 4.2 The matrix of a linear map
- 4.3 Composition of linear maps
- 4.4 Invertible linear maps
- 4.5 The transition matrix
- 4.6 Dual spaces and transpose maps
- 4.7 Exercises
- 5. The Rank of a Matrix
- 5.1 The rank of a matrix
- 5.2 Exercises
- 6. Diagonalization of Linear Operators
- 6.1 Eigenvalues and eigenvectors
- 6.2 Cayley-Hamilton Theorem
- 6.3 Diagonalizability of linear operators
- 6.4 Direct sum of subspaces
- 6.5 Exercises
- 7. Inner Product Spaces and Bilinear Forms
- 7.1 Basic properties of inner product spaces
- 7.2 The simplified Gram-Schmidt orthogonalization
- 7.3 Orthogonal complements
- 7.4 Bilinear forms and Sylvester's law of inertia
- 7.5 Quadratic forms
- 7.6 Exercises
- Solutions and Hints
- Appendix A. Equivalence Relations and Kuratowski-Zorn Lemma
- References
- Index
- 1.1 Arithmetic of complex numbers
- 1.2 Polar form of complex numbers
- 1.3 Polynomials over a field
- 1.4 Irreducible polynomials
- 1.5 Exercises
- 2. Determinants
- 2.1 Evaluating determinants
- 2.2 Exercises
- 3. Vector Spaces and Subspaces
- 3.1 Basic properties of vector spaces
- 3.2 Subspaces
- 3.3 Spanning sets and linear dependence
- 3.4 Bases and dimension
- 3.5 Applications and Sum-Dimension Formula
- 3.6 Quotient spaces
- 3.7 Exercises
- 4. Linear Maps
- 4.1 Linear maps, Dimension Theorem
- 4.2 The matrix of a linear map
- 4.3 Composition of linear maps
- 4.4 Invertible linear maps
- 4.5 The transition matrix
- 4.6 Dual spaces and transpose maps
- 4.7 Exercises
- 5. The Rank of a Matrix
- 5.1 The rank of a matrix
- 5.2 Exercises
- 6. Diagonalization of Linear Operators
- 6.1 Eigenvalues and eigenvectors
- 6.2 Cayley-Hamilton Theorem
- 6.3 Diagonalizability of linear operators
- 6.4 Direct sum of subspaces
- 6.5 Exercises
- 7. Inner Product Spaces and Bilinear Forms
- 7.1 Basic properties of inner product spaces
- 7.2 The simplified Gram-Schmidt orthogonalization
- 7.3 Orthogonal complements
- 7.4 Bilinear forms and Sylvester's law of inertia
- 7.5 Quadratic forms
- 7.6 Exercises
- Solutions and Hints
- Appendix A. Equivalence Relations and Kuratowski-Zorn Lemma
- References
- Index