The number of published treatises on matrices is not large, and so far as we are aware this is the first which develops the subject with special reference to its applications to differential equations and classical mechanics. The book is written primarily for students of applied mathematics who have no previous knowledge of matrices, and we hope that it will help to bring about a wider appreciation of the conciseness and power of matrices and of their convenience in computation. The general scope of the book is elementary, but occasional discussions of advanced questions are not avoided. The sections containing these discussions, which may with advantage be omitted at the first reading, are distinguished by an asterisk.

The first four chapters give an account of those properties of matrices which are required later for the applications. Chapters I to in introduce the general theory of matrices, while Chapter iv is devoted to various numerical processes, such as the reciprocation of matrices, the solution of algebraic equations, and the calculation of latent roots of matrices by iterative methods.

The remainder of the book is concerned with applications. Chapters v and vi deal in some detail with systems of linear ordinary differential equations with constant coefficients, and Chapter vn contains examples of numerical solutions of systems of linear differential equations with variable coefficients.