Linear Algebra (Hardcover, 3, 1998)

Vectors in the Plane and Space.- Vector Spaces.- Examples of Vector Spaces.- Subspaces.- Linear Independence and Dependence.- Finite Dimensional Vector Spaces and Bases.- The Elements of Vector Spaces: A Summing Up.- Linear Transformations.- Linear Transformations: Examples and Applications.- Linear Transformations and Matrices.- Representing Linear Transformations by Matrices.- More on Representing Linear Transformations by Matrices.- Systems of Linear Equations.- The Elements of Eigenvalue and Eigenvector Theory.- Inner Product Spaces.- The Spectral Theorem and Quadratic Forms.- Jordan Canonical Form.- Application to Differential Equations.- The Similarity Problem. Appendix A: Multilinear Algebra and Determinants.