Teorema espectral: operadores autoadjuntos e aplicação.

Abstract

This work is dedicated to the study of conditions for diagonalization of linear Operators, defined in real or complex vector spaces. The main result is the theorem Spectral for Linear Operators, which gives conditions for diagonalization. We will define the previous concepts about: Vector Space, Base, Dimension, Internal Product, Eigenvalues ​​and Autovectors and Autoadjoint Operators. These concepts are used in the Spectral Theorem, where the same tells us that "For every self-adjoint operator T defined from V to V , in a space finite dimensional vector provided with the inner product, there is an orthonormal basis of vectors contained in V formed by eigenvectors of T". As an application, we use the concept of maximum and local minimum and a quadratic form for ranking points of a function of several variables.