  In tensor eigenvalue problems, one is likely to be more interested in
H-eigenvalues of tensors. The largest H-eigenvalue of a nonnegative tensor or
of a uniform hypergraph is the spectral radius of the tensor or of the uniform
hypergraph. We find upper bounds and lower bounds (interlacing inequalities)
for the largest H-eigenvalue of a principal subtensor of a symmetric zero
diagonal tensor that is of even order or nonnegative, as well as lower bounds
for the largest H-eigenvalue of a uniform hypergraph with some vertices or
edges removed. We also investigate similar problems for the least
H-eigenvalues. We give examples to verify the sharpness of the bounds or in
some cases for uniform hypergraphs, we characterize the equality. Particularly,
for a connected linear $k$-uniform hypergraph $G$ with $v\in V(G)$, we give a
sharp lower bound for the spectral radius of $G-v$ in terms of the spectral
radius of $G$ and the degree of $v$ and characterize the extremal hypergraphs,
and show that the maximum spectral radius of the subhypergraphs with one vertex
removed is greater than or equal to the spectral radius of the hypergraph minus
one, which is attained if and only if it is a Steiner system $S(2,k,n)$.
