Distance between real finite dimensional linear subspaces Is there a usual distance between linear subspaces ($V,W$) of an n-dimensional normed vector space with inner product?
In the case of hyper-planes one could use the angle (based on the inner product of the vector space). What can be used in the case of subspaces with lower dimension (not necessarily equal)? e.g. $dim(V)= n-2$ and $dim(W) = n-4$
Thanks

There is, if both subspaces have the same dimension. You can actually make the set of $k$-dimensional subspaces of a vector space $V$ into a metric space (a manifold, in fact) called the Grassmannian, denoted $\mathrm{Gr}(k,V)$. The distance between two subspaces $W$ and $W'$ is then $\|P_W-P_{W'}\|$ where $P_X$ denotes projection onto $X$ and $\|\cdot\|$ is the operator norm.
