Conic and Quadric surfaces

TL;DR

This paper explores the classification of conic and quadric surfaces by analyzing their equations using matrix and spectral theory, addressing fundamental questions about their geometric nature in plane and space.

Contribution

It introduces a method to determine the nature of conic and quadric surfaces through matrix and spectral analysis, providing a systematic approach to their classification.

Findings

Provides a matrix-based method for classifying conic and quadric surfaces.

Clarifies the geometric interpretation of second-degree equations.

Offers solutions to fundamental questions in analytical geometry.

Abstract

There are two problems Analytical Geometry with facing anyone who studies this discipline: define the nature of the locus represented by the general equation 2do degree in two or three variables: That curve represents the plane? What surface is in space? These two problems are posed and solved by applying the study of matrices and spectral theory