ANALYTIC GEOMETRY: points, vectors and matrices

Geometry is one of the oldest branches of mathematics and there is a great deal of information about it, both in the literature and on the web. The creation of analytic geometry is traditionally attributed to René Descartes; however, there were already known works before him in which geometry and algebra were combined. Moreover, Descartes did not employ the geometric concept of vector.

This book develops Euclidean Analytic Geometry of the plane and space from a vector perspective. It is not that there are not several texts on the market with this material; unfortunately those that approach the subject with acceptable rigor (without going into detail on what acceptable means) are out of print and difficult to acquire, and those that are commercial, it is precisely this quality that detracts from their rigor and depth when dealing with the concepts. This work is not intended to redefine the rigor of the subject, but rather to contribute as a modern text with a treatment suitable for students of mathematics or physics, or in its case, for engineering students who wish to complement their courses in physics, linear algebra or calculus in several variables as far as geometric interpretation is concerned.