Complex number, polynomials, matrix, system of equation, Gaussian elimination, vector space, linear transformation, etc. T.M. Aposotol's Calculus Vol. 1 in the calculus sections also introduce topics that is relevant to this area.
A few Americans (exchanged to Sydney) in my third year abstract algebra class told us they couldn't follow because they haven't learnt much complex number. In order to have fun with linear algebra and complex variables in stage 2, it's better to learn complex number now.
- Anton H. and Rorres C. Elementary Linear Algebra - The application version introduced how linear algebra can be applied to Markov Chains, Graph Theory, Games of Strategy, Computer Graphics, Fractals, Chaos, Cryptography, Genetics, etc.
- Axler S. Linear Algebra Done Right - See Axler's page for this.
- Chen W.W.L. Linear Algebra (FREE!) - Read Chapter n's, for all positive integer n<8.
- Chen W.W.L. Miscellaneous Topics in First Year Mathematics (FREE!)
- Dawkins P. Algebra (FREE!)
- Gardner R.B. Linear Algebra (FREE!) - Leave Chapter 6 and 7 to the next stage.
- Joyce D.E. A Short Course on Complex Numbers (FREE!)
- Lang S. Undergraduate Algebra - He's a member of the Bourbaki and wrote many books. Not friendly for beginners, but you should get use to it.
- Lay D.C. Linear Algebra and Its Applications
- Matthews K. Elementary Linear Algebra (FREE!)
- Santos D. Linear Algebra Notes [.pdf] (FREE!)
- Strang G. Linear Algebra and Its Applications
- Wedderburn J.H.M. Lectures on Matrices (FREE!)
- 山东大学数学学院：秦静教授线性代数课件 [.rar] (FREE!)