We analyze the the convergence behavior of block GMRES and characterize the phenomenon of
stagnation which is then related to the behavior of the block FOM method. We generalize the
block FOM method to generate well-defined approximations in the case that block FOM would
normally break down, and these generalized solutions are used in our analysis. This behavior
is also related to the principal angles between the column-space of the previous block GMRES
residual and the current minimum residual constraint space. At iteration $j$, it is shown that the
proper generalization of GMRES stagnation to the block setting relates to the columnspace of the
$j$th block Arnoldi vector. Our analysis covers both the cases of normal iterations as well as block
Arnoldi breakdown wherein dependent basis vectors are replaced with random ones. Numerical
examples are given to illustrate what we have proven, including one constructed (artificially) from
small application problem to demonstrate the validity of the analysis in a less pathological case.
These results are then put into context of some more recent work [Frommer et al. ETNA 2018], which characterizes an entire family 
of block Krylov methods using a generalization of the inner product and norm to the block setting.