This Python script is designed to help users calculate the eigenvalues and eigenvectors of a 3x3 matrix they provide. Additionally, it generates the characteristic equation for the matrix. The script ...

Eigenvector-Eigenvalue Identity Code This code generates a random Hermitian matrix of dimension n and then calculates the norm squared of the elements of the normed eigenvectors, |v i,j | 2. It then ...

An eigenvalue-based characterization of positive realness of transfer functions of a single-input single output time-invariant linear system is derived. Based on this characterization, we propose an ...

Tom Carroll, Jesse Ratzkin, Monotonicity of the First Dirichlet Eigenvalue of the Laplacian on Manifolds of Non-Positive Curvature, Indiana University Mathematics Journal, Vol. 65, No. 1 (2016), pp.

In 1980, Yang and Yau [20] proved the celebrated upper bound for the first eigenvalue on an orientable surface of genus γ . Later Li and Yau [14] gave a simple proof of this bound by introducing the ...

A complete understanding of the limiting behavior of the principal eigenvalue and its eigenfunction is obtained, and new fundamental effects of large degenerate advection and boundary conditions on ...