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"Eigenvalues and Eigenvectors" as a book category would encompass works focused on the theory, computation, and applications of linear transformations and their spectral properties — from introductory linear algebra texts that explain the basic definitions and geometry to advanced monographs on spectral theory, numerical algorithms, and perturbation analysis. Titles in this category would cover proofs and intuition for eigen-decomposition, diagonalization, and singular value decomposition, practical methods for computing eigenpairs (power method, QR, iterative solvers), and domain-specific uses in physics (quantum mechanics, vibrations), engineering (stability, control), data science and machine learning (PCA, spectral clustering), differential equations, and network analysis. Books could range from classroom textbooks and problem guides to applied handbooks with software examples (MATLAB, Python) and research-level treatments addressing infinite-dimensional operators, random matrix theory, or optimization. The category serves students, practicing scientists and engineers, and researchers seeking both conceptual understanding and practical tools for interpreting and manipulating linear operators through their eigenstructure.

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