Einfuhrung in Die Determinantentheorie

This is the third edition of Kowalewski's classic treatise on determinants. The majority of the book concerns properties of determinants of matrices, including special families of matrices, such as symmetric or orthogonal matrices. A main chapter covers the applications to linear and quadratic forms. Kowalewski then turns his attention to matrices associated to one or more functions. An example of such is the Wronskian of a collection of $n$ functions of one variable, which is connected with the theory of $n$th-order ordinary differential equations. Another key example is that of the Fredholm determinant and the associated minors, which are important in Hilbert's approach to the solution of linear integral equations. The third edition finishes with a newly added chapter on elementary divisor theory.