Linear Algebra

This book presents a treatment of principal topics of linear algebra and illustrates the importance of the subject through a variety of applications. The topics include vector spaces, linear transformations and matrices, elementary matrix operations and systems of linear equations, determinants, diagonalization, inner product spaces, canonical forms. In addition there are applications to differential equations, economics, geometry, physics and probability. The second edition uses Gaussian elimination instead of Gauss-Jordan method, reduces the dependence of direct sums, shortens and reorganizes the coverage of diagonalization, develops unitary diagonalization via Schur's theorem as opposed to the more abstract invariant subspaces, interchanges canonical forms and inner product spaces, and features a new subsection which develops motions in the plane.