Matrices and Networks

Related lectures (31)

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

Explores the diagonalization of matrices and the conditions for exact diagonalization, with examples demonstrating the process.

Explains the diagonalization of matrices, criteria, and significance of distinct eigenvalues.

Explores interlacing families of polynomials and 1-sided Ramanujan graphs, focusing on their properties and construction methods.

Explores eigenvalues and eigenvectors, demonstrating their importance in linear algebra and their application in solving systems of equations.

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

Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.

Covers clustering using K-means and LDA, PCA, K-means properties, Fisher LDA, and spectral clustering.

Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.

Covers the criteria for diagonalizing a matrix and provides illustrative examples.