Book for studying Linear Algebra

Solution 1:

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.

Solution 2:

Look for Strang's Introduction to Linear Algebra. It has a feymannesque quality that I could not find in any other textbook. I specially recommend it if you lean toward Computer Science. I am doing a minor in Mathematics and my class uses Friedberg's Linear Algebra. While a very rigorous text, it is also very cold and non motivating. You want to read the novel, go for Strang's. I have also used Leon's Linear Algebra with applications in a previous computational course.

Proving an identity for complete homogenous symmetric polynomials

Show that there is sequence of homeomorphism polynomials on [0,1] that converge uniformly to homeomorphism

Why does $ \frac{2x}{2+x}$ provide a particularly tight lower bound for $\ln(1+x)$ for small positive values of $x$?

Definability in a given structure

Is it possible to prove the axiom of infinity from the real number axioms?

Does $\sum_{k=0}^{\infty}\sin\left(\frac{\pi x}{2^k}\right)$ have a simple form with interesting properties?

Does free functor preserve monomorphism?

What are the rules for the use of dots rather than parentheses in logical formulae?

Intuition behind independence and conditional probability

Prove that a polynomial of degree $d$ has at most $d$ roots (without induction)

Sum of one, two, and three squares

Proving that each graph contains a spanning tree?