Eigenvalues and eigenvectors of a matrix
Helmut Bez, Tony Croft · 2023
This chapter introduces the essential topics and to show how eigenvalues and eigenvectors are calculated. In quantum computation it is relevant to consider cases in which the eigenvalues are all real and the eigenvectors are orthogonal. In the study of quantum computation, the matrices with which we usually work have properties that enable us to be quite specific about the nature of the eigenvalues and eigenvectors. Post-measurement the system is in a state represented by an eigenvector or eigenvectors. In quantum computation it is relevant to consider cases in which the eigenvalues are all real and the eigenvectors are orthogonal.