Subspace iteration

Subspace iteration repeatedly applies a matrix to several independent vectors and orthonormalizes them, converging to a dominant invariant subspace when a spectral gap separates the selected eigenvalue cluster.

A dominant invariant subspace is spanned by eigenvectors whose eigenvalue moduli exceed those outside the subspace.

When several eigenvalues share the largest modulus, normalized power iterates need not converge individually, but every limit lies in their joint invariant subspace.