PENERAPAN ALJABAR LINEAR DALAM PEMODELAN SISTEM DINAMIS: KAJIAN LITERATUR, TEKNIK, EKONOMI, DAN ILMU KOMPUTER

Abstract

This study aims to analyze the application of linear algebra in dynamic system modeling, emphasizing the use of algebraic techniques to understand and solve problems in complex systems. The method employed is a systematic literature review approach, collecting and analyzing relevant literature published within the last ten years. The main focus is on identifying and applying key concepts in linear algebra, such as matrices, vectors, eigenvalues, eigenvectors, singular value decomposition (SVD), and principal component analysis (PCA) in dynamic system analysis. The results indicate that linear algebra plays a highly significant role in various fields of dynamic system modeling, including engineering, economics, and computer science. Eigenvalues are proven effective in analyzing the stability of dynamic systems, while SVD and PCA are useful in reducing the dimensionality of very large systems. Furthermore, linear algebra facilitates multivariate system modeling and the solution of linear differential equation systems that describe system evolution. Nevertheless, not all dynamic systems can be modeled linearly; nonlinear systems require alternative techniques such as numerical methods or Monte Carlo simulation. Future research is encouraged to explore the integration of linear algebra with machine learning methods to improve the accuracy and efficiency of modeling more complex dynamic systems