Corpos com a propriedade dos eixos principais

Abstract

Our goal in this work is to study which fields satisfy the Principal Axis Theorem. In other words, we classify those fields over which the Principal Axis Theorem is valid; that is, all symmetric matrices are orthogonally diagonalizable. In order to achieve this goal, we will introduce fields and their basic properties. We will study the Axiom of Choice and itsequivalent formulations. We will also study ordered fields and prove the Artin{Schreier Theorem. Then we will consider Pythagorean fields and real closed fields. Finally, using the tools that will have been introduced, we will characterize fields with the Principal Axis Property.