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Linear Algebra: An Introduction with Concurrent Examples: v. 2
This book is a readable introduction to linear algebra, starting at an elementary level. It is intended to be useful both for students of pure mathematics who may subsequently pursue more advanced study in this area and for students who require linear algebra and its applications in other subjects. Throughout, stress is placed on applications of the
subject in preference to more theoretical aspects. The book has worked examples on every left-hand page concurrently with the text on the right-hand page, which allows the reader to follow the text uninterrupted. The book is intended to be worked through and learned from, and contains numerous exercises with solutions.
Contents:
Preface
- Part I: 1
Gaussian elimination
- 2
Solutions to simultaneous equations I
- 3
Matrices and algebraic vectors
- 4
Special matrices
- 5
Matrix inverses
- 6
Linear independence and rank
- 7
Determinants
- 8
Solutions to simultaneous equations II
- 9
Vectors in geometry
- 10
Straight lines and planes
- 11
Cross product
- Part II: 12
Basic ideas
- 13
Subspaces of Rn
- 14
Spanning lists, bases, dimension
- 15
Rank
- 16
Linear transformations
- 17
Change of basis
- 18
Eigenvalues and eigenvectors
- 19
Diagonalisation I
- 20
The dot product
- 21
Orthogonality
- 22
Diagonalisation II
- 23
Geometry
- 24
Differential equations
- Answers to exercises
- Sample test paper for part I
- Sample test paper for part II
- Index.
Brief Description:
This enlarged version of the author's A First Course in Linear Algebra provides an introduction to linear algebra, starting at an elementary level. Throughout, emphasis is placed on applications of the subject in preference to more theoretical aspects.
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