




274 pages, 10x7 inches
April
2001 Hardcover
ISBN 1589490126
US$52 

Buy It 

After thirty years
of teaching, the author, a number theorist, has produced
this one semester first course in linear algebra, not
necessarily for math majors. Students will enjoy such a
book that can be read from cover to cover in a semester;
instructors will find every hopedfor result proved.
Abstraction enters gradually. Students learn to use
inner product in R^2, then R^3. Most of the work is done
in R^n. In the last chapter, when students are ready,
vector spaces, including C^n, appear. There are nice
applications such as electrical circuits, Markov
chains... All examples can be done by hand. No time lost
learning software!
To know more about the book please click
on
Preface to Instructors
and/or
Excerpts
from the book. 
Preface
Ch.1. Euclidean space
1.1 The Euclidean plane
1.2 Inner product in R^2
1.3 Three dimensional Euclidean space R^3
1.4 Lines and planes in R^3
1.5 Euclidean space R^n
Exercises
Ch.2. Linear systems and
matrices
2.1 Linear systems
2.2 Matrices
2.3 Row reduction
2.4 General solution of a linear system
2.5 Homogeneous systems
2.6 Electric circuits
Exercises
Ch.3. Linear independence.
Subspaces
3.1 Sum notation
3.2 Linear span and linear independence
3.3 Subspaces of R^n
3.4 General propositions about bases
3.5 Column space. Rank
3.6 Coordinate vectors. Change of coordinates
Exercises
Ch.4. Linear mappings. Matrix
algebra
4.1 Linear mappings
4.2 Onetoone mappings, onto mappings
4.3 Algebraic rules of matrix algebra
4.4 Powers and inverses
4.5 Inverse of a product. Transpose
4.6 Change of basis
4.7 Orthogonal matrices
Exercises
Ch.5. Determinants

5.1
Permutations
5.2 Row reduction
5.3 Expansion by a row or column
5.4 The adjoint
5.5 The determinant of a product
Exercises
Ch.6. Eigenvalues &
eigenvectors
6.1 Finding the eigenvalues and eigenvectors
6.2 Diagonalization
6.3 Further results on eigenvectors &
eigenvalues
6.4 The CayleyHamilton theorem
6.5 Markov chains
6.6 The steady state vector
Exercises
Ch.7. Symmetric
matrices & quadratic forms
7.1 Quadratic forms
7.2 Orthogonal sets
7.3 Orthogonal complement
7.4 Orthogonal diagonalization
7.5 Diagonalizing a quadratic form
7.6 Sylvester's law of inertia
7.7 Quadric curves
Exercises
Ch.8. Vector spaces
8.1 Complex numbers
8.2 Fields
8.3 Vector spaces
8.4 General results about vector spaces
8.5 Inner product spaces
8.6 Fourier series
8.7 Eigenvalues & eigenvectors of matrices over
C
8.8 Linear differential equations
Exercises
Further reading
Answers to selected
exercises 

Roger
Baker gained his Ph.D. in London in 1971. Analytic
number theory, especially the distribution of prime
numbers, is his primary research interest. His monograph
Diophantine Inequalities was published by Oxford
in 1986, and he is the author of about 90 research
papers in wellknown journals. He is currently working
on a graduate text on modular forms. After working for
London University for twenty years, the author moved to
Brigham Young University, Utah, in 1991. In his spare
time he works on his small farm, where visitors can meet
llamas, Jacob sheep, pheasants, and other creatures that
he and his wife Lynnette enjoy.



