Spectral decomposition is a mathematical technique that expresses an operator or matrix in terms of its eigenvalues and eigenvectors, essentially breaking it down into simpler components. This concept is particularly significant in linear algebra and functional analysis, as it allows us to analyze and understand the behavior of operators more easily. By expressing an operator in its spectral form, we can gain insights into its properties, such as stability and symmetry, which are crucial when dealing with different types of operators.
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