Advancements in Linear Algebra: From Theory to Applications

Dr. Raman

Linear Algebra, computational problems, matrix theory

This paper provides a comprehensive exploration of linear algebra and matrix theory, two fundamental areas of mathematics with extensive applications across various scientific and engineering disciplines. We delve into the core concepts of vector spaces, linear transformations, matrices, and eigenvalues, highlighting their theoretical foundations and practical significance. The study also reviews recent advancements in numerical linear algebra, emphasizing the development of efficient algorithms for solving large-scale computational problems. Through a combination of theoretical analysis and practical examples, we demonstrate how linear algebra and matrix theory are pivotal in addressing complex challenges in data science, engineering, and beyond. Our findings underscore the ongoing importance of these mathematical tools in modern research and application, offering insights into future trends and potential innovations in the field.