274 pages, 10x7 inches
April 2001 Hardcover
ISBN 1-58949-012-6


    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 hoped-for 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.


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
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
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
Ch.4. Linear mappings. Matrix algebra
4.1 Linear mappings
4.2 One-to-one 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
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
Ch.6. Eigenvalues & eigenvectors
6.1 Finding the eigenvalues and eigenvectors
6.2 Diagonalization
6.3 Further results on eigenvectors & eigenvalues
6.4 The Cayley-Hamilton theorem
6.5 Markov chains
6.6 The steady state vector
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
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
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 well-known 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.