Finite-Dimensional Spaces: Algebra, Geometry, and Analysis Volume I

This treatise (consisting of the present Vol.I and of Vol.II, to be published) is primarily intended to be a textbook for a core course in mathematics at the advanced undergraduate or the beginning graduate level. The treatise should also be useful as a textbook for selected students in honors programs at the sophomore and junior level. Finally, it should be of use to theoretically inclined scientists and engineers who wish to gain a better understanding of those parts of mathematics that are most likely to help them gain insight into the conceptual foundations of the scientific discipline of their interest.