= Two-column dominant-subspace condition
Let a real <symmetric matrix> have an <orthonormal eigenbasis> $w_1,\ldots,w_n$, with
$$
|\lambda_1|\leq\cdots\leq|\lambda_{n-2}|<
|\lambda_{n-1}|=|\lambda_n|.
$$
Write two starting vectors as
$$
u=\sum_i b_iw_i,
\qquad
v=\sum_i c_iw_i.
$$
For two-column <subspace iteration> to recover
$\operatorname{span}(w_{n-1},w_n)$, the two projections onto that dominant subspace must be independent. The exact condition is
$$
\det\begin{pmatrix}
b_{n-1}&c_{n-1}\\
b_n&c_n
\end{pmatrix}
=b_{n-1}c_n-b_nc_{n-1}\ne0.
$$
Requiring each of the four coefficients to be nonzero does not imply this determinant condition.
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