Eigenvalues and eigenvectors appear in many physical and engineering problems, beginning with the noted study by Euler in 1751 of the kinematics of rigid bodies. From a mathematical point of view, for an operator of a suitable class, acting in a vector space, its point spectrum and associated subspaces refer to its “eigenvalues and eigenvectors”, while the subspaces associated with the continuous spectrum of the operator is said to consist of “eigenfunctions”. The basic ideas will be discussed mostly through examples, in some of which a natural connection with the representation of appropriate groups lurks behind.

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