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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., Comment: 27 pages

This paper is devoted to condition numbers of the total least squares problem with linear equality constraint (TLSE). With novel limit techniques, closed formulae for normwise, mixed and componentwise condition numbers of the TLSE problem are derived. Computable expressions and upper bounds for these condition numbers are also given to avoid the costly Kronecker product-based operations. The results unify the ones for the TLS problem. For TLSE problems with equilibratory input data, numerical experiments illustrate that normwise condition number-based estimate is sharp to evaluate the forward error of the solution, while for sparse and badly scaled matrices, mixed and componentwise condition numbers-based estimates are much tighter., Comment: 19 pages