  This paper is devoted to condition numbers of the multidimensional total
least squares problem with linear equality constraint (TLSE). Based on the
perturbation theory of invariant subspace, the TLSE problem is proved to be
equivalent to a multidimensional unconstrained weighed total least squares
problem in the limit sense. With a limit technique, Kronecker-product-based
formulae for normwise, mixed and componentwise condition numbers of the minimum
Frobenius norm TLSE solution are given. Compact upper bounds of these condition
numbers are provided to reduce the storage and computation cost. All
expressions and upper bounds of these condition numbers unify the ones for the
single-dimensional TLSE problem and multidimensional total least squares
problem. Some numerical experiments are performed to illustrate our results.
