• However, the
subspaces S2=span{x2}, S23=span{x2
, x3}, S24=span{x2 , x4}, S234=span{x2 , x3 , x4} are not A-invariant subspaces since the lower rank
generalized eigenvector x1 of x2 is not in these subspaces.
• To
illustrate, consider the subspace S23. It is an A-invariant subspace if Ax2 Î S23. Since Ax2=l1x2 +x1 , Ax2 Î S23 would
require that x1 be a linear combination of x2 and x3, but this is impossible since x1 is independent of x2 and x3.