Understanding Eigenvalues

In this compilation, two approaches to construct the state space equations of an analog circuit are presented. In the first approach the state matrix A is directly constructed from the circuit inspections. In the second approach, a method is presented through which the zeros of a transfer function are converted into poles, and then the poles are extracted through the circuit eigenvalues. The authors survey some new problems in spectral extremal graph theory. Spectral extremal graph theory mainly studies the spectral properties of various matrices associated with graphs, including adjacency matrix, Laplacian matrix, or signless Laplacian matrix. Some properties of the eigenvalues of some third-order boundary-value-transmission problems are introduced, generated by a differential expression where the coefficients are real-valued and Lebesgue measurable functions on a given interval.