Active spectrum of the power method (source code)

= Active spectrum of the power method

For a <diagonalizable matrix>, the active spectrum consists of <eigenvalues> whose <eigenspaces> have nonzero components of the starting <vector> in its <spectral decomposition>. These components are <orthogonal projections> for a <self-adjoint operator>, but need not be orthogonal projections for a general <diagonalizable matrix>. With a unique largest <modulus> in this active spectrum, the <power method> selects its eigendirection; an exactly absent dominant component is never created in exact arithmetic.