  An orthonormal basis matrix $X$ of a subspace ${\cal X}$ is known not to be
unique, unless there are some kinds of normalization requirements. One of them
is to require that $X^{\rm T}D$ is positive semi-definite, where $D$ is a
constant matrix of apt size. It is a natural one in multi-view subspace
learning models in which $X$ serves as a projection matrix and is determined by
a maximization problem over the Stiefel manifold whose objective function
contains and increases with tr$(X^{\rm T}D)$. This paper is concerned with
bounding the change in orthonormal basis matrix $X$ as subspace ${\cal X}$
varies under the requirement that $X^{\rm T}D$ stays positive semi-definite.
The results are useful in convergence analysis of the NEPv approach (nonlinear
eigenvalue problem with eigenvector dependency) to solve the maximization
problem.
