(1.1) |〈u,v〉| ≤ ‖u‖ ‖v‖. An outline of a proof of this fundamental inequality, when V = R and ‖ · ‖ is the standard Eucledian norm, is given in Exercise 24 of Section 2.7 of [1]. We will give a proof in the general case at the end of this section. LetW be an n dimensional subspace of V and let P : V 7→W be the corresponding projection operator, i.e. if v ∈ V then w = Pv ∈W is the element in W w...

Several computational methods are presented for the rapid extraction of decay time constants from discrete exponential data. Two methods are found to be comparably fast and highly accurate. They are corrected successive integration and a method involving the Fourier transform (FT) of the data and the application of an expression that does not assume continuous data. FT methods in the literature...