Potential Theory
Spectral decomposition is a mathematical technique that expresses a linear operator, such as the discrete Laplace operator, in terms of its eigenvalues and eigenvectors. This method breaks down the operator into simpler components, allowing for a clearer understanding of its properties and behavior, especially in relation to functions defined on discrete spaces like graphs or lattices. By utilizing this approach, one can solve problems involving differential equations or analyze the stability of solutions more effectively.
congrats on reading the definition of Spectral Decomposition. now let's actually learn it.