Linear algebra as the foundation of artificial intelligence algorithms in economic research
DOI:
https://doi.org/10.26565/2786-4995-2026-3-10Keywords:
linear algebra, artificial intelligence, matrix transformations, singular value decomposition, economic forecasting, neural networks, stability of dynamic systems, support vector method, macroeconomic modelingAbstract
The subject of this study is the mathematical framework of linear algebra, which serves as the computational foundation for modern artificial intelligence (AI) algorithms used in macro- and microeconomic analysis, time series forecasting, exchange rate estimation, and the modeling of complex economic systems. The key characteristics of this subject include the multidimensional nature of economic data, the presence of nonlinear dependencies alongside linear operations within algorithmic pipelines (matrix products, singular value decomposition, eigenvalues, and eigenvectors), as well as the need to balance computational efficiency with the interpretability of results.
Problem statement. Despite the rapid spread of neural network and statistical methods for forecasting economic indicators, in most applied studies the linear-algebraic structure of these methods remains implicit, which complicates the informed selection of a model architecture, the assessment of its stability, and the interpretation of the results obtained for economic practice.
Unresolved aspects of the problem. The scientific literature lacks a systematic overview of exactly which linear-algebraic constructs (matrix transformations, decompositions, spectral analysis) underlie specific classes of AI models (recurrent networks, the support vector method, hybrid wavelet models), nor is there a consistent interpretation of the relationship between the eigenvalues of matrices of dynamic systems and the stability of forecasts of macroeconomic indicators.
Purpose of the article. The purpose of this article is to systematize and theoretically justify the role of linear algebra as the methodological and computational basis for artificial intelligence algorithms used in economic research, as well as to develop a generalized framework for the relationship between linear algebraic operations and the stages of economic forecasting.
Presentation of the main material. The article examines the matrix representation of economic data, linear transformation operations (matrix multiplication, singular value decomposition, principal component analysis), spectral analysis of the stability of dynamic economic systems, as well as the linear-algebraic structure of neural network layers, support vector machines (SVM), and hybrid wavelet models, based on an analysis of 18 contemporary scientific sources.
Conclusions. It has been shown that, regardless of the external architectural form (recurrent network, support vector method, hybrid wavelet model), the computational core of AI algorithms in economic research consists of linear algebra operations, and understanding this structure is of practical importance for improving the accuracy, stability, and interpretability of economic forecasts.
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