Matrix of a Linear Transformation Relative to a Preferred Basis (and How You Might Deal with Repeated Eigenvalues and Complex Eigenvalues)

    Abstract

    The question of whether a matrix A can be diagonalized can be described succinctly as follows: Can a basis of eigenvectors be found for the given matrix A? If the answer is Yes, then there is a basis of eigenvectors B = {v 1 Av k = λ k v k for k = 1,2,...,n. It is a useful construction to talk about the idea of the matrix of a linear transformation relative… (More)

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