Delve into the second lecture of Random Matrix Theory and its Applications, presented by Satya Majumdar at the Bangalore School on Statistical Physics - X. Explore key concepts in linear algebra and quantum mechanics, including operators, orthogonal transformations, and eigenvectors. Learn about random matrices, their ensembles, and the Gaussian Ensemble. Examine rotation-invariant ensembles and their properties. Engage with examples, exercises, and a Q&A session to deepen your understanding of this advanced topic in statistical physics.