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Résumé :
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Linear Algebra for Data Science, Machine Learning, and Signal Processing presents a modern and application-oriented introduction to linear algebra, focusing on the mathematical tools most useful in data science, machine learning, and engineering applications. The book begins with fundamental concepts such as vectors, matrices, vector spaces, linear transformations, and matrix operations, ensuring that readers develop a strong conceptual understanding before moving to advanced topics. It emphasizes geometric interpretations of linear algebra concepts, helping readers visualize ideas such as orthogonality, projections, and subspaces. As the material progresses, the book introduces key techniques such as eigenvalues, eigenvectors, singular value decomposition (SVD), and matrix factorizations, explaining how these tools are applied in real-world problems like dimensionality reduction, Principal Component Analysis (PCA), regression, and signal reconstruction. A major focus of the book is connecting theory with computation, showing how algorithms derived from linear algebra are used in modern machine learning systems and large-scale data analysis. Throughout the text, practical examples and exercises highlight how linear algebra supports pattern recognition, data compression, recommendation systems, and optimization problems. Overall, the book aims to bridge the gap between classical linear algebra theory and modern data-driven applications, making it especially valuable for students in mathematics, computer science, data science, and electrical engineering who want to understand both the mathematical foundations and practical uses of linear algebra in today's technological fields.
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