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spectral theory basic concepts and applications pdf
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Spectral theory is a branch of mathematics that studies properties of operators and matrices that are invariant under change of basis. It deals with the decomposition of operators into simpler parts, such as eigenvalues and eigenvectors, and explores the relationships between them. Basic concepts in spectral theory include diagonalization, spectral decomposition, and the spectral theorem. Applications of spectral theory can be found in various fields, such as physics, engineering, and computer science, where it is used to analyze and solve problems involving linear operators and systems. By understanding spectral theory, one can gain insights into the behavior of complex systems and develop tools for solving a wide range of problems in mathematics and its applications.