Diagonalização de operadores e formas canônicas de Jordan

Abstract

The academic work aims to present the theory involved in the Diagonalization of Operators and Jordan Canonical Forms. Such theory provides us with Mathematical tools that enhance and facilitate the processes of numerous abstract developments in the area of exact sciences. Thus, in the course of the work, the basic concepts of Linear Algebra are presented, from the Vector Spaces to the Eigenvalues and Eigenvectors of a Linear Operator. Undertaking the Diagonalization of Real and Complex Operators and then we present some so-called particular operators: normal, self-adjoint, symmetric, hermitian, isometry, among others. The Diagonalization of resembling operators is discussed through the Spectral Theorem, which is divided into two versions, the real and the complex. Additionally, we present the concepts necessary to obtain the Jordan Form of a linear operator that is not diagonalizable. To finish the study, we will epitomize how to obtain the Jordan Form of some operators.