The Double Entry Accounting and Matrix Algebra

Byung T. Ro
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Byung T. Ro: Purdue University

Chapter 7 in The Geometry of Accounting, 2025, pp 151-172 from Springer

Abstract: Abstract In matrix algebra, a matrix is defined as an array of real numbers. An accounting event (transaction) has three intrinsic elements—debit, credit, and size, denoted by d, c, and q in previous chapters. As the monetary quantity of each element is shown by a real number, accounting events can be shown as an array of real numbers, hence as a matrix. This chapter discusses how to construct the matrix of accounting events and examines its features and properties from the perspective of matrices and theories thereof and according to the double entry principle. The geometric settings used to do so are two- and three-dimensional vector spaces with multiple Cartesian coordinates. There are various kinds of matrices, and the chapter focuses on two of them in particular—diagonal matrix and scalar matrix. These two kinds of matrices have features and properties that are consistent with the duality and balance features of accounting events or, more generally, the duality and balance features of double entry accounting.

Date: 2025
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DOI: 10.1007/978-3-031-88892-2_7

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