Linear Algebra by Paul Dawkins
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About this book :-
It explains important ideas like matrices, vectors, and solving systems of equations in a clear and easy way. The book gives lots of examples and practice problems to help students understand the steps. It’s a good choice for learning or reviewing the basics of linear algebra. These notes do assume that the reader has a good working knowledge of basic Algebra. Vector calculus is useful, but not necessary preparation for this book, which attempts to be self-contained.
The book has been written such that instructors can reorder the chapters (using the La- TeX source) in any (reasonable) order and still have a consistent text. The notions of abstract vectors and linear transformations hard and early, while at the same time giving students the basic matrix skills necessary to perform computations. Gaussian elimination is followed directly by an “exploration chapter” on the simplex algorithm to open students minds to problems beyond standard linear systems ones. Vectors in Rn and general vector spaces are presented back to back so that students are not stranded with the idea that vectors are just ordered lists of numbers. Once students see that a linear map is specified by its action on a limited set of inputs, they can already understand what a basis is. All the while students are studying linear systems and their solution sets, so after matrices determinants are introduced. This material can proceed rapidly since elementary matrices were already introduced with Gaussian elimination. Only then is a careful discussion of spans, linear independence and dimension given to ready students for a thorough treatment of eigenvectors and diagonalization. The dimension formula therefore appears quite late, since author prefer not to elevate rote computations of column and row spaces to a pedestal. The book ends with applications–least squares and singular values. It would also be quite easy to spend any extra time on systems of differential equations and simple Fourier transform problems.
Book Detail :-
This book has following details information.
Title:
Linear Algebra by Paul Dawkins
Publisher:
Lamar University
Year:
2011
Pages:
331
Type:
PDF
Language:
English
ISBN-10 #:
N\A
ISBN-13 #:
N\A
License:
N\A
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About Author :-
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Book Contents :-
This book has following table of contents.
1. What is Linear Algebra?
2. Systems of Linear Equations
3. The Simplex Method
4. Vectors in Space, n-Vectors
5. Vector Spaces
6. Linear Transformations
7. Matrices
8. Determinants
9. Subspaces and Spanning Sets
10. Linear Independence
11. Basis and Dimension
12. Eigenvalues and Eigenvectors
13. Diagonalization
14. Orthonormal Bases and Complements
15. Diagonalizing Symmetric Matrices
16. Kernel, Range, Nullity, Rank
17. Least Squares and Singular Values
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