I am trying to solve a problem that is asking for what conditions that make $<A>$ unique. It does not explain what <> represents, but I think it means the column space. A is a matrix where its columns are a subset of the k largest eigenvectors of B.
I do not understand what it means for the column space to be unique. But if I had to guess, I would take it to mean that A is full rank, i.e., the subset of eigenvectors that form A are linearly independent.
Does anyone have a different interpretation?
Edit: Actually I just confirmed that $<A>$ is the column space of A.
The column space is unique as it is defined as the smallest (wrt inclusion) subspace that contains all the columns of $A$ as elements. In this case it also is the set of all linear combinations of columns of $A$, which is minimal (as we can check it is a subspace and any subspace containing the columns must contain their linear combinations).