Brief History of Matrices, As a Tool of Consolidated Financial Statements(*)

Abstract

Consolidation of accounts has always generated problems for accountants and auditors because of its computational difficulties, especially when the subsidiaries have mutual stockholdings, circular stockholdings and indirect stockholdings. The application of mathematics to accounting is not always simple and clear, yet, referring to the fact that accounting has a structure, not obvious a priori, but real vector space in two dimensions, and we can apply methods based on linear algebra, classic technique of matrices and less traditional methods such as Markov chains. These methods are irreplaceable to understand and describe the logical groups and consolidations. We can go further in the analysis of relationships between companies in a group and we can have the ambition to rationalize and then to optimize these relationships using, generally, the optimal forms of mathematics, mathematics of symmetrical shapes, and the properties of the Euler characteristic and the Pythagorean regular polyhedrons, especially. Firstly we recall briefly the historical principles of application of matrix methods to the accounting, and the classical and non-classical methods to solve the general problem of consolidated financial statements.

Keywords

• Consolidation - Consolidated Statements - Space Vector - Groups of companies - Holding - Matrices - regular polyhedron.