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Abstract
Modern healthcare increasingly relies on linear algebra as a key framework that facilitates accurate data handling, computational efficiency, and better diagnostic and treatment decisions. This paper presents a comprehensive review of the role of linear algebra in healthcare systems, emphasizing both theoretical foundations and practical applications. Fundamental concepts such as matrices, vector spaces, eigenvalues, and decompositions are discussed in the context of medical data processing and algorithmic design. Matrix-based methods are shown to be central to medical imaging, particularly MRI and CT reconstruction, where techniques such as Fourier transforms, singular value decomposition, and compressed sensing enable high-resolution image generation with reduced acquisition time.
In predictive analytics, linear algebra facilitates the development of regression models, dimensionality-reduction techniques, and machine learning algorithms used for disease diagnosis and patient risk stratification. The paper also explores applications in genomics, where matrix factorization and clustering methods help analyze high-dimensional gene expression data. Additionally, linear algebra supports optimization of healthcare operations, enabling better resource allocation and workflow planning. Case studies on MRI reconstruction and disease prediction illustrate the effectiveness of matrix-driven approaches. Overall, the findings underscore the expanding importance of linear algebra in enabling data-driven, intelligent, and patient-centered healthcare solutions.
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