Linear Algebra Done Right

This text is intended for a second course in linear algebra aimed at students interested in pursuing mathematics; it would thus follow a general course on matrices and computations. The approach is novel, banishing determinants to the end of the book, and focusing on the central concerns of linear algebra: understanding the structure of a linear map from a vector space onto itself. The existence of eigenvalues on complex vector spaces is proven without use of determinants. The easily grasped concept of an invariant subspace provides motivation for the study of eigenvalues and eigenvectors and leads naturally to the generalized eigenvectors. Here the minimal polynomial plays the dominant role usually played by the characteristic polynomial.