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For a finite intensity matrix B the final limit of its transition matrix exp(tB) exists. This is a well-known fact in the realm of continous-time Markov processes where it is proven by probability theoretic means. A simple proof is presented with help of a Tauberian theorem of complex analytic functions which is used also in [2] to proof the prime number theorem. Furthermore the final limit is computed.

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A determinant formula for the euclidean distance between a point and a linear subspace is presented. As a consequence determinant formulas are derived for: a positive semidefinite, hermitian matrix; the loss value of multilinear regression; the multiple linear regression coefficient.