This is a standard book on Linear Algebra for science and engineering students. It covers the usual topics, including the Jordan canonical form, a topic that is omitted in many recent books at this level.
The book reminded me of Strang's Linear Algebra and its Applications : it contains essentially the same material, albeit in a slighly different order. Like Strang, the authors discuss linear difference and differential equations at some length, which should be useful to students in applied sciences. Unlike Strang, however, Kwak and Hong follow a more traditional line of presentation, with numbered definitions, lemmas, theorems, and examples. This may make it easier for the student to use the book as a reference. The exposition is clear but the style is not as chatty as Strang's.
In summary, the book can be safely used as the basis for a course on Linear Algebra for the intended audience.
Preface to the First Edition * Preface to the Second Edition * Linear Equations and Matrices * Determinants * Vector Spaces * Linear Transformations * Inner Product Spaces * Diagonalization * Complex Vector Spaces * Jordan Canonical Forms * Quadratic Forms * Selected Answers and Hints * Bibliography * Index