Eigenvalue problems are mathematical scenarios where one seeks to determine the scalar values (eigenvalues) associated with a linear transformation represented by a matrix, and the corresponding non-zero vectors (eigenvectors) that satisfy the equation $$A\mathbf{v} = \lambda\mathbf{v}$$. These problems are fundamental in various fields such as physics, engineering, and applied mathematics, as they help analyze systems' behavior under transformations, stability, and vibrations.
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