This textbook on linear algebra includes the key topics of the usual topics, such as complex vector spaces, complex inner products, the Spectral theorem for normal operators, dual spaces, the minimal polynomial, the Jordan canonical form, and the rational canonical form, are covered, along with a chapter on determinants at the end of the book. In addition, there is material throughout the text on linear differential equations and how it integrates with all of the important concepts in linear algebra.This book has several distinguishing features that set it apart from other linear algebra texts. For example, Gaussian elimination is used as the key tool in getting at eigenvalues, it takes an essentially determinant-free approach to linear algebra, and systems of linear differential equations are used as frequent motivation for the reader.