  This paper deals with a homoskedastic errors-in-variables linear regression
model and properties of the total least squares (TLS) estimator. We partly
revise the consistency results for the TLS estimator previously obtained by the
author [18]. We present complete and comprehensive proofs of consistency
theorems. A theoretical foundation for construction of the TLS estimator and
its relation to the generalized eigenvalue problem is explained. Particularly,
the uniqueness of the estimate is proved. The Frobenius norm in the definition
of the estimator can be substituted by the spectral norm, or by any other
unitarily invariant norm; then the consistency results are still valid.
