Linear Algebra by Arnold J. Insel, Lawrence E. Spence, Stephen H. Friedberg (2002, Hardcover, Subsequent Edition)

This top-selling, theorem-proof book presents a careful treatment of the principle topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate. Chapter topics cover vector spaces, linear transformations and matrices, elementary matrix operations and systems of linear equations, determinants, diagonalization, inner product spaces, and canonical forms. For statisticians and engineers.