Lecture
This lecture covers the Laplacian matrix in electric and mechanical networks, including its spectral characterization and properties. It explains the Laplacian matrix without using graphs, examples of Laplacians in physical systems, and the Laplacian matrix of undirected weighted graphs. The lecture also discusses consensus in continuous time, electrical networks of resistors, and properties of Laplacian matrices, such as zero column sum and spectrum analysis. It concludes with the implications of Laplacian matrices in networked control systems.