**1. Introduction**

290 Macro to Nano Spectroscopy

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There are a great variety of processing the analytical spectroscopy data, especially useful in multicomponent systems [Ewing et al., 1953; Garrido et al., 2004; Lykkesfeld, 2001; Oka et al., 1991; Sánchez & Kowalski, 1986]. These methods essentially are based on different strategies of mathematical strategies including specific formalism of mathematical statistics and of matrix algebra [Garrido et al., 2004; Szabadai, 2005]. The matrix-based methods reffer to quantitative analysis [Bosch-Reigh et al., 1991; Garrido et al., 2008; Li et al., 2011; Lozano et al., 2009; Ruckenbusch et al., 2006; Szabadai, 2005], to determination of the number of independent chemical equilibria in multicomponent systems [Szabadai, 2005] and for correction the action of various perturbing factors such as stray light or backgroud absorption [Burnius, 1959; Fox & Mueller, 1950; Melnick, 1952; Morton & Stubbs, 1946, 1947, 1948; Owen, 1995; Page & Berkovitz, 1943; Szabadai, 2005].

In the present chapter original approaches of matrix treatment of the aforementioned items are presented, with special consideration to the simultaneous assay of compounds in a mixter, to backgruond correction procedures and to the standard addition method in a generalized form.
