Explore the third installment of Spectral Graph Theory in this graduate-level lecture from Carnegie Mellon University's "CS Theory Toolkit" course. Delve into the eigenvalues of the Laplacian and Markov operator, along with associated formulas. Learn from Professor Ryan O'Donnell as he covers key concepts including the K Operator, theorems, eigenvectors, notation, expansion, and corollaries. Utilize Spielman's "Spectral and Algebraic Graph Theory" book as a supplementary resource for this 22-minute lecture, which forms part of a comprehensive semester-long program on math and CS fundamentals for theoretical computer science research.