Eigenvalues and Eigenvectors

Recall that an n × n matrix B is similar to an n × n matrix A if there is an invertible n × n matrix P such that B = P −1 AP. Our objective now is to determine under what conditions an n × n matrix is similar to a diagonal matrix. In so doing we shall draw together all of the notions that have been previously developed. Unless otherwise specified, A will denote an n × n matrix over ℝ or ℂ.