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Related lectures (31)

Page 3 of 4

Matrix Operations: Definitions and Examples

Covers the basic operations on matrices, including addition, scalar multiplication, and matrix multiplication.

Pseudorandomness: Expander Mixing Lemma

Explores pseudorandomness and the Expander Mixing Lemma in the context of d-regular graphs.

Pseudo Randomness in Graphs

Explores pseudo randomness in graphs using eigenvalues and polynomials, emphasizing the significance of bunched roots and common interlacers.

Networks: Computer Representation

Covers the concept of adjacency matrix and adjacency lists for representing networks.

Matrix Operations: Definitions and Properties

Covers matrix operations, including dimensions, transposition, and multiplication properties.

Consensus in Networked Control Systems

Explores consensus in networked control systems through graph weight design and matrix properties.

Isogeny Graphs: Eigenvalues and Cryptography

Explores isogeny graphs of supersingular elliptic curves, showing optimal mixing times for random walks and applications to cryptography.

Networked Control Systems: Graph Theory and Stochastic Matrices

Explores graph theory, stochastic matrices, consensus algorithms, and spectral properties in networked control systems.

Expander Graphs: Properties and Eigenvalues

Explores expanders, Ramanujan graphs, eigenvalues, Laplacian matrices, and spectral properties.

Convergence of Adjacency Matrix: Spectral Properties and Consensus Theorem

Explores the convergence of adjacency matrix powers and consensus theorem for primitive and stochastic matrices, emphasizing spectral properties and networked control systems.