Matrix diagonalization is the process of taking a square matrix and converting
it into a special type of matrix called diagonal matrix that shares the same
fundamental properties of the underlying matrix. To diagonalize a matrix is also
equivalent to find the matrix's eigenvalues, which turn out to be precisely the
entries of the diagonalized matrix. The remarkable relationship between a
diagonalized matrix, eigenvalues, and eigenvectors follows from the mathematical
identity that a square matrix