Examining Role of Mathematics in Hardware Engineering: Relationship Between Linear Algebra and Embedded Systems

Abstract

Linear algebra is often regarded as an abstract branch of mathematics, however, it has a myriad of implementations in the real world, particularly in the field of computer science and hardware engineering. Embedded systems, which represent small computing units integrated into various devices that we use on a daily basis, heavily rely on mathematical models in order to function properly. This article examines the role that fundamental linear algebra concepts such as vectors, matrices, eigenvalues and linear transformations play in embedded systems. Particularly, it outlines practical implementation of these concepts in signal processing, control systems, robotics and image processing, highlighting how they support core tasks and enable efficient performance. By bridging mathematical theory with engineering practice, this paper shows why linear algebra is indispensable for modern embedded system design and development.