So I'm taking Linear Algebra in college. However, I'm not getting the grades I want and I have sort of difficulties using my teacher's book: it has very formal explanations and a strong lack of examples. I'm looking for a book that has a good explanation of the content and also solved exercises (which is a very important thing that I'm missing). So here is a list of books my college has:
Calculus: T. M. Apostol 1994 Vol. I. and Vol.II Reverté
Linear Algebra and Its Applications: G. Strang 1988 3rd ed. Academic Press
Linear Algebra: S. Lipschutz 1994 Schaum's Outline Series. McGraw-Hill
What is in your opinion the best book for self-study? (I'm going to repeat the examinations next semester but I'll be studying on my own.) If there is a better book than the ones on this list please tell me. Thanks!!
EDIT:
I study in a Portuguese-speaking country and we use a Portuguese book.
The contents of the course are:
Systems of linear equations. Gaussian elimination. Vectors and matrices. Inverse matrices. Linear spaces and linear transformations. Linear independence, bases and dimension. Kernel and range of a linear transformation. Applications to linear differential equations. Inner products and norms, orthogonal bases and Gram-Schmidt orthogonalization, orthogonal complements and projection onto subspaces. Applications to equations of straight lines and planes. Least squares approximations. Determinants and their applications. Eigenvalues and eigenvectors. Invariant subspaces. Diagonalization of matrices. Jordan forms. Hermitian, skew Hermitian, and unitary transformations. Quadratic forms.
Best Answer
I can heartily recommend Linear Algebra, as I am the author. Coverage is what you asked for, with an emphasis on improving students's mathematical maturity, including lots of examples using computations. It is totally Free and you can also get a physical book from Amazon if you prefer that. There are completely solved answers for all exercises, on the web page (click on the question for the answer and click on the answer for the question). In addition, the beamer slides do different examples from the book, so that's twice as many examples right there.